Caputo-Hadamard approach applications: solvability for an integro-differential problem of Lane and Emden type

Abstract

The present paper is dealing with a new direction in the Caputo-Hadamrd approach. It is concerned with the solvability of an integro differential problem of type Lane and Emden. The studied problem involves Caputo-Hadamard derivative with new different fractional orders. The main results of existence of solutions are based on the contraction principle of Banach, however, for the existence of solutions, the use of Scheafer fixed point theorem is applied to prove the result. Three examples are discussed at the end of this work.