Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Equation with Iterated Fractional Integrals Conditions

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...

Some Iterated Integrals in the Fractional Calculus

On the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...

Nontrivial solutions for a higher fractional differential equation with fractional multi-point boundary conditions

This paper investigates the existence and uniqueness of nontrivial solutions to a class of fractional nonlocal multi-point boundary value problems of higher order fractional differential equation, this kind of problems arise from viscoelasticity, electrochemistry control, porous media, electromagnetic and signal processing of wireless communication system. Some sufficient conditions for the exi...

Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions

where q : [a,b] → R is a continuous function, and the zeros a and b of every solution y(t) are consecutive. Since then, many generalizations of the Lyapunov inequality have appeared in the literature (see [–] and the references therein). Recently, the research of Lyapunov-type inequalities for fractional boundary value problem has begun. In [], Ferreira investigated a Lyapunov-type inequali...