Analysis of Sequential Caputo Fractional Differential Equations versus Non-Sequential Caputo Fractional Differential Equations with Applications

Numerical Methods for Sequential Fractional Differential Equations for Caputo Operator

To obtain the solution of nonlinear sequential fractional differential equations for Caputo operator two methods namely the Adomian decomposition method and DaftardarGejji and Jafari iterative method are applied in this paper. Finally some examples are presented to illustrate the efficiency of these methods. 2010 Mathematics Subject Classification: 65L05, 26A33

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

On Caputo type sequential fractional differential equations with nonlocal integral boundary conditions

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract This paper investigates a boundary value problem of Caputo type sequential fractional differential equations supplemented with nonlocal Riemann-Liouville f...

Existence and Uniqueness of Solutions for Caputo-hadamard Sequential Fractional Order Neutral Functional Differential Equations

In this article, we study the existence and uniqueness of solutions for Hadamard-type sequential fractional order neutral functional differential equations. The Banach fixed point theorem, a nonlinear alternative of LeraySchauder type and Krasnoselski fixed point theorem are used to obtain the desired results. Examples illustrating the main results are presented. An initial value integral condi...

Practical Stability of Caputo Fractional Differential Equations by Lyapunov Functions

The practical stability of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given fractional differential equation. Comparison results using this definition for scalar fractional differential equations are presented. Several ...