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Strichartz’s Radon transforms for mutually orthogonal affine planes and fractional integrals Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-09 Yingzhan Wang
In this paper, we study the general orthogonal Radon transform \({R}_{j,k}^p\) first studied by R.S. Strichartz in [21]. The main conclusions include the sharp existence conditions for \({R}_{j,k}^pf\) on Lebesgue spaces, the relation formulas connecting our transforms with the fractional integrals and Semyanistyi integrals, through which a number of explicit inversion formulas are obtained when f
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On approximate controllability of multi-term time fractional measure differential equations with nonlocal conditions Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-08 Amadou Diop
The purpose of this paper is to investigate the existence of mild solutions and approximate controllability of a class of multi-term time-fractional measure differential equations of hyperbolic type involving nonlocal conditions in Hilbert spaces. The approximate controllability is demonstrated by utilizing fundamental tools, namely: \((\beta ,\gamma _{k})\)-resolvent family, measure functional (H
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Considerations regarding the accuracy of fractional numerical computations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-08 Octavian Postavaru, Flavius Dragoi, Antonela Toma
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Wellposedness and stability of fractional stochastic nonlinear heat equation in Hilbert space Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-08 Zineb Arab, Mahmoud Mohamed El-Borai
In this work, we interest in the study of the wellposedness and the stability of fractional stochastic nonlinear heat equation in the Hilbert space \( L^{2}(0,1) \); perturbed by a trace-class noise and driven by the fractional Laplacian. Precisely, we use the fixed point theorem to prove the wellposedness of the problem. Moreover, we prove the \( p^{th} \)-moment exponential stability and the almost
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On differentiability of solutions of fractional differential equations with respect to initial data Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-05 Mikhail I. Gomoyunov
In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order \(\alpha \in (0, 1)\). As initial data, we consider a pair consisting of an initial point, which does not necessarily coincide with the inferior limit of the fractional derivative, and a function that determines the values of a solution on the interval from this inferior
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Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-04 Kai Diethelm, Ha Duc Thai, Hoang The Tuan
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Trace regularity for biharmonic evolution equations with Caputo derivatives Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-04 Paola Loreti, Daniela Sforza
Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky systems. The order \(\alpha \) of the Caputo fractional derivative belongs to the interval (1, 2). We achieve such result for a suitable class of weak solutions.
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Non-stationary zipper $$\alpha $$ α -fractal functions and associated fractal operator Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-03 Sangita Jha, Saurabh Verma, Arya K. B. Chand
The present paper aims to introduce a new concept of a non-stationary scheme for the so called fractal functions. Here we work with a sequence of maps for the zipper iterated function systems (IFS). We show that the proposed method generalizes the existing stationary interpolant in the sense of IFS. Further, we study the elementary properties of the proposed interpolant and calculate its box and Hausdorff
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Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$ s → 0 + Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-04 Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara
We study the asymptotic behaviour of the renormalised s-fractional Gaussian perimeter of a set E inside a domain \(\Omega \) as \(s\rightarrow 0^+\). Contrary to the Euclidean case, as the Gaussian measure is finite, the shape of the set at infinity does not matter, but, surprisingly, the limit set function is never additive.
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Multi-term fractional oscillation integro-differential equations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-03 Tran Dinh Phung, Dinh Thanh Duc, Vu Kim Tuan
In this paper we study solvability of multi-term Caputo and Riemann-Liouville fractional oscillation integro-differential equations. We show that these equations have unique solutions in the space of functions with square average power growth and derive the solutions in explicit forms.
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Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-02 Xiangcheng Zheng
We investigate the variable-exponent Abel integral equations and corresponding fractional Cauchy problems. The main contributions are twofold: We provide a novel inverse technique to convert the first-kind Volterra integral equation of variable exponent to a second-kind one, which, to our best knowledge, is not available in the literature; Based on this transformation, we carry out rigorous analysis
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A fractional version of the recursive Tau method for solving a general class of Abel-Volterra integral equations systems Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-02 Younes Talaei, Sedaghat Shahmorad, Payam Mokhtary, Amin Faghih
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Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-08-01 Xingqiu Zhang, Zhuyan Shao, Qiuyan Zhong
In this article, based on further investigation of the properties of the Green function, together with a fixed point theorem due to Avery-Peterson, height functions on special bounded sets are constructed to obtain the existence of triple positive solutions for higher-order fractional integral boundary value problems. The nonlinearity permits singularities both on the time and the space variables.
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Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-07-26 Łukasz Płociniczak, Mateusz Świtała
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Some estimates for $$p$$ p -adic fractional integral operator and its commutators on $$p$$ p -adic Herz spaces with rough kernels Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-07-20 Naqash Sarfraz, Muhammad Aslam
In this note we study the boundedness of \(p\)-adic fractional integral operator with rough kernels on \(p\)-adic Herz spaces. Moreover, we establish Lipschitz estimates for commutators of \(p\)-adic fractional integral operator with rough kernels on Herz spaces. In addition, we also obtain central bounded mean oscillations\((C{\dot{M}}O)\) estimate for commutators of \(p\)-adic fractional integral
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Exact solutions of fractional oscillation systems with pure delay Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-07-07 Li Liu, Qixiang Dong, Gang Li
In this paper we study the exact solutions of a class of fractional delay differential equations. We consider the fractional derivative of the order between 1 and 2 in the sense of Caputo. In the first part, we introduce two novel matrix functions, namely, the generalized cosine-type and sine-type delay Mittag-Leffler matrix functions. Then we obtain the explicit solutions for the linear homogeneous
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Vallée-Poussin theorem for fractional functional differential equations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-07-07 Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
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Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-28 Mokhtar Kirane, Ahmad Z. Fino
In this paper, we consider the Cauchy problem in \(\mathbb {R}^N\), \(N\ge 1\), for semi-linear Schrödinger equations with space–time fractional derivatives. We discuss the nonexistence of global \(L^1\) or \(L^2\) weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local \(L^1\) or \(L^2\) weak solutions
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Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-28 Rachid Echarghaoui, Mohamed Masmodi
In this paper, we consider the following problem involving fractional Laplacian operator $$\begin{aligned} \left\{ \begin{array}{ll} (-\varDelta )^{\alpha } u=|u|^{2_{\alpha }^{*}-2}u+\lambda |u|^{q-2}u, &{} \text{ in } \varOmega , \\ u=0, &{} \text{ on } \partial \varOmega , \end{array}\right. \end{aligned}$$ where \(\varOmega \) is a smooth bounded domain in \({\mathbb {R}}^{N}\), \(\lambda >0\)
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Numerical conservation laws of time fractional diffusion PDEs Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-23 Angelamaria Cardone, Gianluca Frasca-Caccia
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Spectral analysis of multifractional LRD functional time series Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-22 M. Dolores Ruiz-Medina
Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario,
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Fractional characteristic functions, and a fractional calculus approach for moments of random variables Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-15 Živorad Tomovski, Ralf Metzler, Stefan Gerhold
In this paper we introduce a fractional variant of the characteristic function of a random variable. It exists on the whole real line, and is uniformly continuous. We show that fractional moments can be expressed in terms of Riemann–Liouville integrals and derivatives of the fractional characteristic function. The fractional moments are of interest in particular for distributions whose integer moments
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Riemann-Liouville derivatives of abstract functions and Sobolev spaces Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-08 Dariusz Idczak
We introduce and study fractional Sobolev spaces of functions taking their values in a Banach space. Our approach is based on Riemann-Liouville derivative. In this regard, paper is a continuation of the paper [D. Idczak, S. Walczak, Fractional Sobolev spaces via Riemann-Liouville derivatives, J. of Function Spaces and Appl. 2013 (2013), Art. ID 128043, 15 pp.], where real-valued functions are investigated
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A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-07 Yong Zhou, Jia Wei He
In this paper, we consider a Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. An elementary fact shows that semi-infinite interval is not compact, the classical Ascoli-Arzelà theorem is not valid. In order to establish the global existence criteria, we first generalize Ascoli-Arzelà theorem into the semi-infinite interval. Next, we introduce
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Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-03 Nguyen Minh Dien, Erkan Nane, Nguyen Dang Minh, Dang Duc Trong
In a Hilbert space, we consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable t and the space fractional function of the self-adjoint positive unbounded operator. We consider various cases of global Lipschitz and local Lipschitz source with time-singular coefficient. These sources are generalized of the well–known fractional equations such as
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Anisotropic variable Campanato-type spaces and their Carleson measure characterizations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-03 Long Huang, Xiaofeng Wang
Let \(p(\cdot ):\ {\mathbb {R}^n}\rightarrow (0,\infty )\) be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on \({\mathbb {R}^n}\). In this article, the authors introduce the anisotropic variable Campanato-type spaces and give some applications. Especially, using the known atomic and finite atomic characterizations of anisotropic
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Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-03 Subhash Chandra, Syed Abbas
The goal of this article is to study the box dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions on \([0,1]\times [0,1]\). We prove that the box dimension of the mixed Katugampola fractional integral having fractional order \((\alpha =(\alpha _1,\alpha _2);~ \alpha _1>0, \alpha _2>0)\) of two-dimensional continuous functions on \([0,1]\times [0,1]\) is still
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Stability and stabilization of short memory fractional differential equations with delayed impulses Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-01 Dongpeng Zhou, Xia Zhou, Qihuai Liu
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Construction and analysis of series solutions for fractional quasi-Bessel equations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-01 Pavel B. Dubovski, Jeffrey A. Slepoi
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Stability analysis of fractional differential equations with the short-term memory property Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-02 Xudong Hai, Yongguang Yu, Conghui Xu, Guojian Ren
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Monte Carlo method for fractional-order differentiation extended to higher orders Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-02 Nikolai Leonenko, Igor Podlubny
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Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-02 Quanqing Li, Meiqi Liu, Houwang Li
In this article, we focus on the following fractional Choquard equation involving upper critical exponent $$\begin{aligned} \varepsilon ^{2s}(-\varDelta )^su+V(x)u=P(x)f(u)+\varepsilon ^{\mu -N}Q(x)[|x|^{-\mu }*|u|^{2_{\mu ,s}^*}]|u|^{2_{\mu ,s}^*-2}u, \ x \in {\mathbb {R}}^N, \end{aligned}$$ where \(\varepsilon >0\), \(02s\), \(0<\mu
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Optimal feedback control for a class of fractional evolution equations with history-dependent operators Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-06-01 Yongjian Liu, Zhenhai Liu, Sisi Peng, Ching-Feng Wen
In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators
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Fractional Euler numbers and generalized proportional fractional logistic differential equation Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-27 Juan J. Nieto
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Wright functions of the second kind and Whittaker functions Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-27 Francesco Mainardi, Richard B. Paris, Armando Consiglio
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Fractional integral operators on Orlicz slice Hardy spaces Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-23 Kwok-Pun Ho
This paper gives the mapping properties of the fractional integral operators on Orlicz slice Hardy spaces. We use the extrapolation theory for Hardy type spaces to obtain this result. In particular, our result yields the mapping properties of the fractional integral operators on Hardy slice spaces.
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Radial symmetry and Hopf lemma for fully nonlinear parabolic equations involving the fractional Laplacian Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-16 Miaomiao Cai, Fengquan Li, Pengyan Wang
In this paper, we consider fully nonlinear parabolic problems involving the fractional Laplacian. Hopf type lemmas for both on bounded domain \(\varOmega \) with smooth boundary and half space are obtained. When \(\varOmega \) is a ball or the whole space, we obtain the radial symmetry results of positive solutions. Our results are an extension of Li-Nirenberg [19], Li-Chen [18] and Wang-Chen [24]
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Exterior controllability properties for a fractional Moore–Gibson–Thompson equation Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-13 Carlos Lizama, Mahamadi Warma, Sebastián Zamorano
The three concepts of exact, null and approximate controllabilities are analyzed from the exterior of the Moore–Gibson–Thompson equation associated with the fractional Laplace operator subject to the nonhomogeneous Dirichlet type exterior condition. Assuming that \(b>0\) and \(\alpha -\frac{\tau c^2}{b}>0\), we show that if \(00\). However, we prove that for \(0
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Asymptotic profile for a two-terms time fractional diffusion problem Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-13 Marcello D’Abbicco, Giovanni Girardi
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The similarity method and explicit solutions for the fractional space one-phase Stefan problems Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-13 Sabrina D. Roscani, Domingo A. Tarzia, Lucas D. Venturato
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Weighted estimates for operators of fractional integration of variable order in generalized variable Hölder spaces Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-09 Alexey Karapetyants, Evelyn Morales
The paper is devoted to weighted estimates for operators of fractional integration of variable order of Bergman type in generalized variable Hölder spaces of holomorphic functions on the unit disc \( {\mathbb {D}} \). Due to the choice of the weight, we can include in consideration the case when the real part of the complex power of the operator degenerates. We prove the estimates of Zygmund type for
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Hölder regularity for non-autonomous fractional evolution equations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-03 Jia Wei He, Yong Zhou
This paper concerns a Hölder regularity result for non-autonomous fractional evolution equations (NFEEs) of the form \(^C\!D^\alpha _t u(t)+A(t)u(t)=f(t)\) in the sense of Caputo’s fractional derivative. Under the assumption of the Acquistapace-Terremi conditions, we get a representation of solution that is closer to standard integral equation. A pair of families of solution operators will be constructed
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Delsarte equation for Caputo operator of fractional calculus Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-03 Hassan Emamirad, Arnaud Rougirel
A fractional order variant of the Delsarte equation is investigated involving the Caputo differential derivative. Solvability of the resulting fractional hyperbolic Cauchy problem is achieved in the sense of distributions. A regularity result shows that the solution may be a function of time. Rigorous Delsarte representations are established. The symmetry between the fractional operators acting on
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Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-05-03 Hui Zhang, Fanhai Zeng, Xiaoyun Jiang, George Em Karniadakis
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Unified predictor–corrector method for fractional differential equations with general kernel functions Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-29 Guo-Cheng Wu, Hua Kong, Maokang Luo, Hui Fu, Lan-Lan Huang
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Infinitely many large solutions to a variable order nonlocal singular equation Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-27 Sekhar Ghosh, Dumitru Motreanu
The paper establishes the existence of infinitely many large energy solutions for a nonlocal elliptic problem involving a variable exponent fractional \(p(\cdot )\)-Laplacian and a singularity, provided a positive parameter incorporated in the problem is sufficiently small. A variational method can be implemented for an associated problem obtained by truncation related to the singularity. A comparison
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Mixed stochastic heat equation with fractional Laplacian and gradient perturbation Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-25 Mounir Zili, Eya Zougar
We introduce a new stochastic heat equation with a mixed operator, which is a combination of the standard Laplacian, a fractional Laplacian and the gradient operator, driven by an additive Gaussian noise which is white in time and in space. We establish the existence of the solution and we study its behavior with respect to the time variable. In particular, we establish sharp two-sided interesting
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The fractional variation and the precise representative of $$BV^{\alpha ,p}$$ B V α , p functions Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-25 Giovanni E. Comi, Daniel Spector, Giorgio Stefani
We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019). We provide a general analysis of the distributional space \(BV^{\alpha ,p}({\mathbb {R}}^n)\) of \(L^p\) functions, with \(p\in [1,+\infty ]\), possessing finite fractional variation of order \(\alpha \in (0,1)\)
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Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-25 Yingjie Liang, Yue Yu, Richard L. Magin
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Asymptotics of the Mittag-Leffler function $$E_a(z)$$ E a ( z ) on the negative real axis when $$a \rightarrow 1$$ a → 1 Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-20 Richard Paris
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Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-20 Xiao-Li Ding, Juan J. Nieto, Xiaolong Wang
In this paper, we investigate the solution of multi-term time-space fractional partial delay differential-algebraic equations (MTS-FPDDAEs) with Dirichlet boundary conditions defined on a finite domain. We use Laplace transform method to give the solutions of multi-term time fractional delay differential-algebraic equations (MTS-FDDAEs). Then, the technique of spectral representation of the fractional
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Dynamical repulsive fractional potential fields in 3D environment Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-21 Stéphane Victor, Kendric Ruiz, Pierre Melchior, Serge Chaumette
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Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$ L 2 ( R , C M ) Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-19 M. Younus Bhat, Aamir H. Dar
A generalization of Mallat’s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of \({\mathbb {R}}\) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the
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An eigenvalue problem in fractional h-discrete calculus Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-19 F. M. Atıcı, J. M. Jonnalagadda
In this paper, we prove existence of solutions for an eigenvalue problem in the fractional h-discrete calculus. Dirichlet type boundary conditions are considered. Several properties for Green’s function of the associated problem are proven. A fixed point theorem in Cone theory is a main tool to obtain sufficient conditions on upper and lower bounds for eigenvalues of the boundary value problem so that
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Stochastic solutions of generalized time-fractional evolution equations Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-19 Christian Bender, Yana A. Butko
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between the parameters of the equation and the distribution of the underlying stochastic processes, as well as discuss different classes of processes providing stochastic
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On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-19 Nguyen Minh Dien
The aim of this paper is to investigate the existence of mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition. Unlike previous papers, in the current paper, we assume that the source function of the problem may have a singularity. The existence results are proven via the Schaefer, nonlinear Leray–Schauder alternatives and Banach fixed point theorems
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Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-18 Binjie Li, Hao Luo, Xiaoping Xie
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is firstly established by using variational approach and Mittag-Leffler function. Then several optimal error estimates are derived with low regularity data. Finally, numerical experiments are conducted to verify the theoretical
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The fractional-order Lorenz-type systems: A review Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-18 Ivo Petráš
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The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-18 Vladyslav Litovchenko
In the class of discontinuous unbounded initial functions with an integrable singularity, we consider the Cauchy problem for the pseudodifferential equation of local action of moving objects in the corresponding Riesz gravitational field. The fundamental solution to this problem is the Cauchy probability distribution of the force of local interaction between these objects. An explicit form of this
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Monte Carlo method for fractional-order differentiation Fract. Calc. Appl. Anal. (IF 3.451) Pub Date : 2022-04-18 Nikolai Leonenko, Igor Podlubny