On coupled systems of fractional impulsive differential equations by using a new Caputo-Fabrizio fractional derivative

Stability of Solutions to Impulsive Caputo Fractional Differential Equations

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

Implicit Fractional Differential Equations via the Liouville–Caputo Derivative

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.

Reachability Of Fractional Continuous-Time Linear Systems Using The Caputo-Fabrizio Derivative

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...

Existence Theory for Impulsive Partial Hyperbolic Functional Differential Equations Involving the Caputo Fractional Derivative

In this paper we investigate the existence and uniqueness of solutions of a class of partial impulsive hyperbolic differential equations with fixed time impulses involving the Caputo fractional derivative. Our main tool is a fixed point theorem.