Existence of Solutions for Nonlocal Boundary Value Problem of Hadamard Fractional Differential Equations

Subramanian Muthai̇ah,Nandha Gopal Thangaraj,Manigandan Murugesan

doi:10.31197/atnaa.579701

Abstract

We investigate the existence and uniqueness of solutions for Hadamard fractional differential equations with non-local integral boundary conditions, by using the Leray Schauder nonlinear alternative, Leray Schauder degree theory, Krasnoselskiis fixed point theorem, Schaefers fixed point theorem, Banach fixed point theorem, Nonlinear Contractions. Two examples are also presented to illustrate our results.

Highlights

Fractional differential equations have increased extensive consideration from both hypothetical and the applied perspectives as of late years
We investigate the existence and uniqueness of solutions for Hadamard fractional differential equations with nonlocal integral boundary conditions, by using the Leray-Schauder nonlinear alternative, Leray Schauder degree theorem, Krasnoselskiis fixed point theorem, Schaefers fixed point theorem, Banach fixed point theorem, Nonlinear Contractions
It has seen that the greater part of the work on the point is concerned about RiemannLiouville or Caputo type fractional differential equation

Summary

Introduction

Fractional differential equations have increased extensive consideration from both hypothetical and the applied perspectives as of late years. 163 referred to the hypothesis of fractional derivatives and integrals and applications to differential equations of fractional order. It has seen that the greater part of the work on the point is concerned about RiemannLiouville or Caputo type fractional differential equation. Other than these fractional derivatives, another sort of fractional derivatives established in the literature is the fractional derivative because of Hadamard made known to in 1892 [12], differs from the aforementioned derivatives in the sense that the kernel of the integral in the definition of Hadamard derivative contains a logarithmic function of an arbitrary exponent.

Preliminaries

Examples