the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

Abstract In this work we deal with a uniqueness result of solutions for class fractional differential equations involving the Caputo-Fabrizio derivative. We provide on global convergence successive approximations.

In this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, special of C-F derivative is used in time direction and compact difference operator space direction. Second, discuss convergence proposed method L 1 ...

In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo–Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of...

We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider which susceptible and infected populations evolve according different orders. a model based on Caputo derivative, for we establish existence results of solutions. Furthermore, investigate Caputo–Fabrizio operator, provide solutions equilibria. Both can be framed context SIS with...

In this paper, we consider fractional differential equations with the new derivative involving a nonsingular kernel, namely, Caputo-Fabrizio derivative. Using successive approximation method, prove an extension of Picard-Lindelöf existence and uniqueness theorem for derivative, which gives set conditions, under initial value problem has unique solution.

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and local discontinuous Galerkin (LDG) space. Stability convergence are demonstrated specific choice of numerical fluxes. Finally, efficiency accuracy verified experiments.

In this paper, we investigate the numerical study of nonlinear Fredholm integro-differential equation with fractional Caputo-Fabrizio derivative. We use Hermite wavelets and collocation technique to approximate exact solution by reducing a algebraic system. Furthermore, apply method on certain examples check its accuracy validity.