On Caputo-Hadamard fractional differential equations with nonlocal Hadamard fractional integral conditions

Muthaiah Subramanian; Sargunam Muthu; Ramasamy Sivasamy; Thangaraj Nandha Gopal

Muthaiah Subramanian KPR Institute of Engineering and Technology, Coimbatore, India.
Sargunam Muthu DMI-ST.Eugene University, Chipata Campus, Zambia
Ramasamy Sivasamy M.Kumarasamy College of Engineering, Karur, India.
Thangaraj Nandha Gopal Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India.

Abstract

This paper is concerned with the existence and uniqueness of solutions for the boundary value problem of the Caputo-Hadamard fractional differential equation supplemented with nonlocal Hadamard fractional integral boundary conditions. The existence results are obtained employing fixed point theorems due to Leray-Schauder nonlinear alternative and Krasnoselskiis, whereas the uniqueness of solution is established via the Contraction mapping principle. The obtained results are well illustrated by examples.