Nonlocal Fractional Boundary Value Problems Involving Mixed Right and Left Fractional Derivatives and Integrals

Fractional Boundary Value Problems with Multiple Orders of Fractional Derivatives and Integrals

In this article we study a new class of boundary value problems for fractional differential equations and inclusions with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. The Sadovski’s fixed point theorem is applied in the single-valued case while, in multi-valued case, the nonlinear alternative for contractive maps is u...

Solvability of Nonlocal Fractional Boundary Value Problems

Variational Iteration Method for A Boundary Value Problem with Left and Right Fractional Derivatives

This article studies the variational framework for a boundary value problem involving in left and right fractional derivatives. It presents the sufficient conditions and the absolute error between the approximate solutions and exact solutions. The method is easily computable and quite efficient. Several examples are given to verify the reliability and efficiency of it.

Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab

The term fractional calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. In a letter to L’Hospital in 1695 Leibniz raised the following question (Miller and Ross...

Boundary Value Problems for Nonlinear Fractional Differential Equations and Inclusions with Nonlocal and Fractional Integral Boundary Conditions

Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. These characteristics of the fractional derivatives make the fractional-order models more realistic and practical than the classical integer-order models. In recent years, boundary value problems for nonlinear fractional differential equations have been ad...