Existence and asymptotic behaviour for the time-fractional Keller-Segel model for chemotaxis
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DOI: 10.1002/mana.201700237
Abstract: One of the most important systems for understanding chemotactic aggregation is the Keller–Segel system. We consider the time‐fractional Keller–Segel system of order α∈(0,1). We prove an existence result with small initial data in a class… read more here.
Keywords: asymptotic behaviour; fractional keller; time fractional; keller ... See more keywords
Asymptotic behavior of solutions to space‐time fractional diffusion‐reaction equations
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DOI: 10.1002/mma.4033
Abstract: This article discusses the analyticity and the long-time asymptotic behavior of solutions to space-time fractional diffusion equations in R d . By a Laplace transform argument, we prove that the decay rate of the solution… read more here.
Keywords: asymptotic behavior; solutions space; time fractional; space time ... See more keywords
A time‐fractional competition ecological model with cross‐diffusion
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DOI: 10.1002/mma.6260
Abstract: This paper is concerned with some mathematical and numerical aspects of a Lotka‐Volterra competition time‐fractional reaction‐diffusion system with cross‐diffusion effects. First, we study the existence of weak solutions of the model following the well‐known Faedo‐Galerkin… read more here.
Keywords: diffusion; model; time fractional; cross diffusion ... See more keywords
Regularization of a backward problem for the inhomogeneous time‐fractional wave equation
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DOI: 10.1002/mma.6285
Abstract: In this paper, we consider a backward problem for an inhomogeneous time‐fractional wave equation in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the… read more here.
Keywords: inhomogeneous time; problem; time fractional; problem inhomogeneous ... See more keywords
A new approach to solving multiorder time‐fractional advection–diffusion–reaction equations using BEM and Chebyshev matrix
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DOI: 10.1002/mma.6352
Abstract: In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order time-fractional partial differential equations; nonlinear and linear in respect to spatial and temporal variables, respectively. Fractional derivatives… read more here.
Keywords: approach solving; diffusion; time fractional; time ... See more keywords
On the wave solutions of time‐fractional Sawada‐Kotera‐Ito equation arising in shallow water
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DOI: 10.1002/mma.6763
Abstract: A widescale description of various phenomena in science and engineering such as physics, chemical, acoustics, control theory, finance, economics, mechanical engineering, civil engineering, and social sciences is well described by nonlinear fractional differential equations (NLFDEs).… read more here.
Keywords: fractional sawada; equation; time fractional; kotera ito ... See more keywords
Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity
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DOI: 10.1002/mma.6850
Abstract: A time fractional initial boundary value problem of mixed parabolic–elliptic type is considered. The domain of such problem is divided into two subdomains. A reaction–diffusion parabolic problem is considered on the first domain, and on… read more here.
Keywords: time; parabolic elliptic; problem; singularity ... See more keywords
Nonnegative solutions to time fractional Keller–Segel system
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DOI: 10.1002/mma.6880
Abstract: We establish the existence of nonnegative weak solutions to time fractional Keller–Segel system with Dirichlet boundary condition in a bounded domain with smooth boundary. Since the considered system has a cross‐diffusion term and the corresponding… read more here.
Keywords: keller segel; system; solutions time; segel system ... See more keywords
Approximate solutions for stochastic time‐fractional reaction–diffusion equations with multiplicative noise
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DOI: 10.1002/mma.6925
Abstract: In this paper, we consider the approximate solutions of time‐fractional reaction–diffusion equations forced by multiplicative noise on a bounded domain. When the diffusion is large, one can approximate the solutions of the stochastic time‐fractional reaction–diffusion… read more here.
Keywords: time; fractional reaction; time fractional; reaction diffusion ... See more keywords
Analysis of time‐fractional dynamical model of romantic and interpersonal relationships with non‐singular kernels: A comparative study
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DOI: 10.1002/mma.6929
Abstract: The analysis of interpersonal relationships has started to become popular in the last few decades. Interpersonal relationships exist in many ways, including family, friendship, job, and clubs. In this manuscript, we have implemented the homotopy… read more here.
Keywords: interpersonal relationships; singular kernels; comparative study; non singular ... See more keywords
Numerical simulation for time‐fractional nonlinear reaction–diffusion system on a uniform and nonuniform time stepping
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DOI: 10.1002/mma.7114
Abstract: In this article, two nonstandard high‐order schemes on a uniform and nonuniform time stepping combined with the multi‐parameter exponential fitting technique (MPEF) have been developed to solve the time‐fractional nonlinear reaction–diffusion system. The first method… read more here.
Keywords: time; time stepping; nonuniform time; uniform nonuniform ... See more keywords