Numerical approach to differential equations of fractional order

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

Numerical and Analytical Treatment of Differential Equations of Fractional Order

Study on stability analysis of distributed order fractional differential equations with a new approach

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

A Numerical Method for Solving Fuzzy Differential Equations With Fractional Order

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

Numerical Simulations for Variable-order Fractional Nonlinear Delay Differential Equations

In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate u...