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Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-07-15 Junan Shi, Hongchao Jia, Dachun Yang
Let \(p,q\in [1,\infty )\), s be a nonnegative integer, \(\alpha \in \mathbb {R}\), and \(\mathcal {X}\) be \(\mathbb {R}^n\) or a cube \(Q_0\subsetneqq \mathbb {R}^n\). In this article, the authors introduce the localized special John–Nirenberg–Campanato spaces via congruent cubes, \(jn_{(p,q,s)_{\alpha }}^{\textrm{con}}(\mathcal {X})\), and show that, when \(p\in (1,\infty )\), the predual of \(jn_{(p
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On Taylor’s formulas in fractional calculus: overview and characterization for the Caputo derivative Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-07-08 Roberto Nuca, Matteo Parsani
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Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-07-01 Rongrong Tian, Jinlong Wei
We study the fractional Fokker-Planck-Kolmogorov equation with the fractional index \(\alpha \in [1,2)\) and use a vector-valued Calderón-Zygmund theorem to obtain the existence and uniqueness of \(L^p([0,T];{{\mathcal {C}}}_b^{\alpha +\beta }({{\mathbb {R}}}^d))\cap W^{1,p}([0,T];{{\mathcal {C}}}_b^\beta ({{\mathbb {R}}}^d))\) solution under the assumptions that the drift coefficient and nonhomogeneous
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A necessary and sufficient conditions for the global existence of solutions to fractional reaction-diffusion equations on $$\mathbb {R}^{N}$$ Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-07-01 Soon-Yeong Chung, Jaeho Hwang
A necessary and sufficient condition for the existence or nonexistence of global solutions to the following fractional reaction-diffusion equations $$\begin{aligned} {\left\{ \begin{array}{ll} u_{t}=\Delta _{\alpha } u + \psi (t)f(u),\,\,&{} \text{ in } \mathbb {R}^{N}\times (0,\infty ),\\ u(\cdot ,0)=u_{0}\ge 0,\,\,&{} \text{ in } \mathbb {R}^{N}, \end{array}\right. } \end{aligned}$$ has not been
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Qualitative properties of fractional convolution elliptic and parabolic operators in Besov spaces Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-21 Veli Shakhmurov, Rishad Shahmurov
The maximal \(B_{p,q}^{s}\)-regularity properties of a fractional convolution elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal elliptic equation is sectorial in \( B_{p,q}^{s}\) and also is a generator of an analytic semigroup. Moreover, well-posedeness of nonlocal fractional parabolic equation in Besov spaces is obtained. Then by using the \(B_{p
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An approximation theoretic revamping of fractal interpolation surfaces on triangular domains Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-18 P. Viswanathan
The theory of fractal surfaces, in its basic setting, asserts the existence of a bivariate continuous function defined on a triangular domain. The extant literature on the construction of fractal surfaces over triangular domains use certain assumptions for the construction and deal primarily with the interpolation aspects. Working in the framework of fractal surfaces over triangular domains, this note
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Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-17 Fan Yang, Ying Cao, XiaoXiao Li
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Fractional difference inequalities for possible Lyapunov functions: a review Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-12 Yiheng Wei, Linlin Zhao, Xuan Zhao, Jinde Cao
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A high order predictor-corrector method with non-uniform meshes for fractional differential equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-12 Farzaneh Mokhtarnezhadazar
This article proposes a predictor-corrector scheme for solving the fractional differential equations \({}_0^C D_t^\alpha y(t) = f(t,y(t)), \alpha >0\) with non-uniform meshes. We reduce the fractional differential equation into the Volterra integral equation. Detailed error analysis and stability analysis are investigated. The convergent order of this method on non-uniform meshes is still 3 though
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Continuous-time MISO fractional system identification using higher-order-statistics Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-11 Manel Chetoui, Mohamed Aoun, Rachid Malti
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Fractional order control for unstable first order processes with time delays Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-10 Cristina I. Muresan, Isabela Birs
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Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-10 Gaigai Qin, Xing Fu
Let \(({{\mathcal {X}}},d,\mu )\) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \(I_\beta \) associated with admissible functions and its commutators. Similarly to \(I_\beta \), corresponding results for Calderón–Zygmund
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Mittag-Leffler stability and Lyapunov stability for a problem arising in porous media Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-05 Jamilu Hashim Hassan, Nasser-eddine Tatar, Banan Al-Homidan
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A review of constitutive models for non-Newtonian fluids Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-04 HongGuang Sun, Yuehua Jiang, Yong Zhang, Lijuan Jiang
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On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-06-03 Lin Li, Huo Tao, Stepan Tersian
In this paper, we establish the existence of standing wave solutions for a class of nonlinear fractional Schrödinger-Poisson system involving nonlinearity with subcritical and critical growth. We suppose that the potential V satisfies either Palais-Smale type condition or there exists a bounded domain \(\varOmega \) such that V has no critical point in \(\partial \varOmega \). To overcome the “lack
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Stability analysis of discrete-time tempered fractional-order neural networks with time delays Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-30 Xiao-Li Zhang, Yongguang Yu, Hu Wang, Jiahui Feng
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Fractional differential equations of Bagley-Torvik and Langevin type Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-23 J. R. L. Webb, Kunquan Lan
Nonlinear fractional equations for Caputo differential operators with two fractional orders are studied. One case is a generalization of the Bagley-Torvik equation, another is of Langevin type. These can be confused as being the same but because fractional derivatives do not commute these are different problems. However it is possible to use some common methodology. Some new regularity results for
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Principal curves to fractional m-Laplacian systems and related maximum and comparison principles Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-20 Anderson L. A. de Araujo, Edir J. F. Leite, Aldo H. S. Medeiros
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Pricing European option under the generalized fractional jump-diffusion model Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-16 Jingjun Guo, Yubing Wang, Weiyi Kang
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On variable-order fractional linear viscoelasticity Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-13 Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Andrea Mentrelli
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Well-posedness and stability of a fractional heat-conductor with fading memory Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-10 Sebti Kerbal, Nasser-eddine Tatar, Nasser Al-Salti
We consider a problem which describes the heat diffusion in a complex media with fading memory. The model involves a fractional time derivative of order between zero and one instead of the classical first order derivative. The model takes into account also the effect of a neutral delay. We discuss the existence and uniqueness of a mild solution as well as a classical solution. Then, we prove a Mittag-Leffler
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Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-10 Neha Gupta, Arun Kumar, Nikolai Leonenko, Jayme Vaz
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Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-06 Xuan X. Xi, Yong Zhou, Mimi Hou
In this paper, we study a class of backward problems for nonlinear fractional super-diffusion equations in Banach spaces. We consider the time fractional derivative in the sense of Caputo type. First, we establish some results for the existence of the mild solutions. Moreover, we obtain regularity results of the first order and fractional derivatives of mild solutions. These conclusions are mainly
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On the convergence of the Galerkin method for random fractional differential equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-06 Marc Jornet
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Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-03 Lihong Zhang, Xiaofeng Nie
In this paper, we prove Hopf’s lemma for the Logarithmic Laplacian. At first, we introduce the strong minimum principle. Then Hopf’s lemma for the Logarithmic Laplacian in the ball is proved. On this basis, Hopf’s lemma of the Logarithmic Laplacian is extended to any open set with the property of the interior ball. Finally, an example is given to explain Hopf’s lemma can be applied to the study of
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Non-confluence of fractional stochastic differential equations driven by Lévy process Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-05-03 Zhi Li, Tianquan Feng, Liping Xu
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Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-29 Emilia Bazhlekova
An initial-boundary value problem for the multi-term time-fractional wave equation on a bounded domain is considered. For the largest and smallest orders of the involved Caputo fractional time-derivatives, \(\alpha \) and \(\alpha _m\), it is assumed \(1<\alpha <2\) and \(\alpha -\alpha _m\le 1\). Subordination principle with respect to the corresponding single-term time-fractional wave equation of
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Monotone iterative technique for multi-term time fractional measure differential equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-17 Haide Gou, Min Shi
In this paper, we investigate the existence and uniqueness of the S-asymptotically \(\omega \)-periodic mild solutions to a class of multi-term time-fractional measure differential equations with nonlocal conditions in an ordered Banach spaces. Firstly, we look for suitable concept of S-asymptotically \(\omega \)-periodic mild solution to our concern problem, by means of Laplace transform and \((\beta
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A tempered subdiffusive Black–Scholes model Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-09 Grzegorz Krzyżanowski, Marcin Magdziarz
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Nonnegative solutions of a coupled k-Hessian system involving different fractional Laplacians Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-09 Lihong Zhang, Qi Liu, Bashir Ahmad, Guotao Wang
This paper studies the following coupled k-Hessian system with different order fractional Laplacian operators: $$\begin{aligned} {\left\{ \begin{array}{ll} {S_k}({D^2}w(x))-A(x)(-\varDelta )^{\alpha /2}w(x)=f(z(x)),\\ {S_k}({D^2}z(x))-B(x)(-\varDelta )^{\beta /2}z(x)=g(w(x)). \end{array}\right. } \end{aligned}$$ Firstly, we discuss decay at infinity principle and narrow region principle for the k-Hessian
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Estimates for $$p$$ -adic fractional integral operators and their commutators on $$p$$ -adic mixed central Morrey spaces and generalized mixed Morrey spaces Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-08 Naqash Sarfraz, Muhammad Aslam, Qasim Ali Malik
In this paper, we define the \(p\)-adic mixed Morrey type spaces and study the boundedness of \(p\)-adic fractional integral operators and their commutators on these spaces. More precisely, we first obtain the boundedness of \(p\)-adic fractional integral operators and their commutators on \(p\)-adic mixed central Morrey spaces. Moreover, we further extend these results on \(p\)-adic generalized mixed
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Subordination results for a class of multi-term fractional Jeffreys-type equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-04 Emilia Bazhlekova
Jeffreys equation and its fractional generalizations provide extensions of the classical diffusive laws of Fourier and Fick for heat and particle transport. In this work, a class of multi-term time-fractional generalizations of the classical Jeffreys equation is studied. Restrictions on the parameters are derived, which ensure that the fundamental solution to the one-dimensional Cauchy problem is a
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Collage theorems, invertibility and fractal functions Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-04-03 María A. Navascués, Ram N. Mohapatra
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Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-26 Hengameh Tamimi, Somayeh Saiedinezhad, Mohammad Bagher Ghaemi
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Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-26 Jinyi Sun, Chunlan Liu, Minghua Yang
The paper is concerned with the three-dimensional Boussinesq-Coriolis equations with Caputo time-fractional derivatives. Specifically, by striking new balances between the dispersion effects of the Coriolis force and the smoothing effects of the Laplacian dissipation involving with a time-fractional evolution mechanism, we obtain the global existence of mild solutions to Cauchy problem of three-dimensional
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Transformations of the matrices of the fractional linear systems to their canonical stable forms Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-26 Tadeusz Kaczorek, Lukasz Sajewski
A new approach to the transformations of the matrices of the fractional linear systems with desired eigenvalues is proposed. Conditions for the existence of the solution to the transformation problem of the linear system to its asymptotically stable controllable and observable canonical forms with desired eigenvalues are given and illustrated by numerical examples of fractional linear systems.
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Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-26 Armen M. Jerbashian, Spartak G. Rafayelyan, Joel E. Restrepo
This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [3, 4] or Addendum to [22]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for functions
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Relative controllability of linear state-delay fractional systems Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-25 Nazim I. Mahmudov
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Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-25 Leijie Qiao, Wenlin Qiu, M. A. Zaky, A. S. Hendy
In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution problems. A theta-type (\(\theta \)-type) convolution quadrature rule is derived to approximate the nonlocal integral term in the problem under consideration, such that \(\theta \in (\frac{1}{2},1)\), which remains untreated in the literature. The proposed
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-22 Jacky Cresson, Anna Szafrańska
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Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q \in (1,2)$$ Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-20 Truong Vinh An, Vasile Lupulescu, Ngo Van Hoa
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Rich phenomenology of the solutions in a fractional Duffing equation Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-20 Sara Hamaizia, Salvador Jiménez, M. Pilar Velasco
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Sum of series and new relations for Mittag-Leffler functions Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-19 Sarah A. Deif, E. Capelas de Oliveira
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-11 Hassan Askari, Alireza Ansari
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Global optimization of a nonlinear system of differential equations involving $$\psi $$ -Hilfer fractional derivatives of complex order Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-11 Pradip Ramesh Patle, Moosa Gabeleh, Vladimir Rakočević
In this paper, a class of cyclic (noncyclic) operators of condensing nature are defined on Banach spaces via a pair of shifting distance functions. The best proximity point (pair) results are manifested using the concept of measure of noncompactness (MNC) for the said operators. The obtained best proximity point result is used to demonstrate existence of optimum solutions of a system of differential
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Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-05 Pawan Kumar Mishra, Vinayak Mani Tripathi
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Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-03-04 Nikola Kosturski, Svetozar Margenov
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Analysis of a class of completely non-local elliptic diffusion operators Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-29 Yulong Li, Emine Çelik, Aleksey S. Telyakovskiy
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Discrete convolution operators and equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-27 Rui A. C. Ferreira, César D. A. Rocha
In this work we introduce discrete convolution operators and study their most basic properties. We then solve linear difference equations depending on such operators. The theory herein developed generalizes, in particular, the theory of discrete fractional calculus and fractional difference equations. To that matter we make use of the so-called Sonine pairs of kernels.
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Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-27 Zuomao Yan
We study the approximate optimal control for a class of fractional stochastic hemivariational inequalities with non-instantaneous impulses driven by Rosenblatt process in a Hilbert space. Firstly, a suitable definition of piecewise continuous mild solution is introduced, and by using stochastic analysis, properties of \(\alpha \)-order sine and cosine family and Picard type approximate sequences, we
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Optimal control of fractional non-autonomous evolution inclusions with Clarke subdifferential Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-27 Xuemei Li, Xinge Liu, Fengzhen Long
In this paper, the non-autonomous fractional evolution inclusions of Clarke subdifferential type in a separable reflexive Banach space are investigated. The mild solution of the non-autonomous fractional evolution inclusions of Clarke subdifferential type is defined by introducing the operators \(\psi (t,\tau )\) and \(\phi (t,\tau )\) and V(t), which are generated by the operator \(-\mathcal {A}(t)\)
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A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-26 C. L. Frota, M. A. Jorge Silva, S. B. Pinheiro
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Schrödinger-Maxwell equations driven by mixed local-nonlocal operators Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-26 Nicolò Cangiotti, Maicol Caponi, Alberto Maione, Enzo Vitillaro
In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then
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The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-26 Paulo Mendes Carvalho Neto, Renato Fehlberg Júnior
In this work we study the Riemann-Liouville fractional integral of order \(\alpha \in (0,1/p)\) as an operator from \(L^p(I;X)\) into \(L^{q}(I;X)\), with \(1\le q\le p/(1-p\alpha )\), whether \(I=[t_0,t_1]\) or \(I=[t_0,\infty )\) and X is a Banach space. Our main result provides necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral from \(L^p(t_0
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Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-23 Zhiwei Hao, Libo Li, Long Long, Ferenc Weisz
Let \(0
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Operational matrix based numerical scheme for the solution of time fractional diffusion equations Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-23 S. Poojitha, Ashish Awasthi
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Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-22 Ravshan Ashurov, Rajapboy Saparbayev
This study investigates the inverse problem of determining the right-hand side of a telegraph equation given in a Hilbert space. The main equation under consideration has the form \((D_{t}^{\rho })^{2}u(t)+2\alpha D_{t}^{\rho }u(t)+Au(t)=p( t)q+f(t)\), where \(0
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Generalized Krätzel functions: an analytic study Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-22 Ashik A. Kabeer, Dilip Kumar
The paper is devoted to the study of generalized Krätzel functions, which are the kernel functions of type-1 and type-2 pathway transforms. Various analytical properties such as Lipschitz continuity, fixed point property and integrability of these functions are investigated. Furthermore, the paper introduces two new inequalities associated with generalized Krätzel functions. The composition formulae
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On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-22 Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan D. Repovš
We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there
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Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise Fract. Calc. Appl. Anal. (IF 2.5) Pub Date : 2024-02-21 Zhiqiang Li, Yubin Yan
We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The equation involves the \(\psi \)-Caputo derivative of order \(\alpha \in (0,1)\) and the spectral fractional Laplacian of order \(\beta \in (\frac{1}{2},1]\). The existence and uniqueness of the mild solution are proved in a suitable Banach space by using the