Existence and uniqueness of solutions for system of Hilfer\u2013Hadamard sequential fractional differential equations with two point boundary conditions

Warissara Saengthong,Sotiris K Ntouyas,Ekkarath Thailert

doi:10.1186/s13662-019-2459-8

Abstract

In this paper, we study existence and uniqueness of solutions for a system of Hilfer–Hadamard sequential fractional differential equations via standard fixed point theorems. The existence is proved by using the Leray–Schauder alternative, while the existence and uniqueness by the Banach contraction mapping principle. Illustrative examples are also discussed.

Highlights

Fractional differential equations have been applied in many fields such as physics, chemistry, biology, engineering, and so on
Motivated by the research going on in this direction, in this paper, we study existence and uniqueness of solutions for a new class of systems of Hilfer–Hadamard sequential fractional differential equations
3 Existence and uniqueness results we prove existence and uniqueness of solutions for a system of Hilfer– Hadamard sequential fractional differential equations with boundary conditions (1) and (2)

Summary

Introduction

Fractional differential equations have been applied in many fields such as physics, chemistry, biology, engineering, and so on. Alsaedi et al [23] studied the existence of solutions for a Riemann–Liouville coupled system of nonlinear fractional integro-differential equations given by Ahmad et al [25] studied the existence and uniqueness of solutions for the following boundary value problem of nonlinear Caputo sequential fractional differential equations:

Results

Conclusion