The Caputo-Fabrizio definition of the fractional derivative is applied to analysis of the positivity and reachability of continuous-time linear systems. Necessary and sufficient conditions for the reachability of standard and positive fractional continuous-time linear systems are established. INTRODUCTION A dynamical system is called positive if its trajectory starting from any nonnegative init...

The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated ...

Given an injective closed linear operator A defined in a Banach space X, and writing CFDtα the Caputo–Fabrizio fractional derivative of order α∈(0,1), we show that unique solution abstract Cauchy problem (∗)CFDtαu(t)=Au(t)+f(t),t≥0, where f is continuously differentiable, given by first u′(t)=Bαu(t)+Fα(t),t≥0;u(0)=−A−1f(0), family bounded operators Bα constitutes Yosida approximation Fα(t)→f(t)...

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.

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

In this paper, we simulate a maize streak virus (MSV) epidemic model using the Caputo-Fabrizio fractional derivative. We solve nonlinear fractional-order of MSV recently proposed efficient numerical method. perform several graphical simulations to explore dynamics. The investigations justify usefulness scheme in epidemiology. type generalization and implementation method are key features study.

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.

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.