相关论文: Solving fractional Hantavirus model: A new approac…
We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
In this paper we present analytical solution of a fractional order predator-prey model, where prey grows logistically and predation occurs following type II response function, by homotopy perturbation method. Numerical solutions are…
A generalized model of the spread of the Hantavirus in mice populations is presented on the basis of recent observational findings concerning the movement characteristics of the mice that carry the infection. The factual information behind…
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
The efficient numerical solution of fractional differential equations has been recently tackled through the definition of Fractional HBVMs (FHBVMs), a class of Runge-Kutta type methods. Corresponding Matlab (c) codes have been also made…
In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
We investigate the regional gradient observability of fractional sub-diffusion equations involving the Caputo derivative. The problem consists of describing a method to find and recover the initial gradient vector in the desired region,…
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a…
This paper deals with the existence, multiplicity, minimal complexity and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V.…
This work develops and analyzes a novel fractional-order chemostat system (FOCS) with a Caputo fractional derivative (CFD) featuring a sliding memory window and periodic boundary conditions (PBCs), designed to model microbial pollutant…
This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional…
In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. In…
This paper explores Barenblatt solutions of the time-fractional porous medium equation, characterized by a Caputo-type time derivative. Employing an integral equation approach, we rigorously prove the existence of these solutions and…
This study presents a novel high-order numerical method designed for solving the two-dimensional time-fractional convection-diffusion (TFCD) equation. The Caputo definition is employed to characterize the time-fractional derivative. A weak…
Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…