Nonlocal Fractional Hybrid Boundary Value Problems Involving Mixed Fractional Derivatives and Integrals via a Generalization of Darbo’s Theorem

Solvability of Nonlocal Fractional Boundary Value Problems

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...

Nonlocal Boundary Value Problems for Hybrid Fractional Differential Equations and Inclusions of Hadamard Type

This paper investigates the existence of solutions for nonlocal boundary value problems of nonlinear hybrid fractional differential equations and inclusions of Hadamard type. We make use of fixed point theorems due to Dhage [7], [8] to obtain the existence results. We also discuss some examples for illustration of the main results.

Solvability of Periodic Boundary-value Problems for Second-order Nonlinear Differential Equation Involving Fractional Derivatives

This article concerns the existence of solutions to periodic boundaryvalue problems for second-order nonlinear differential equation involving fractional derivatives. Under certain linear growth condition of the nonlinearity, we obtain solutions, by using coincidence degree theory. An example illustrates our results.

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...