The Existence and Uniqueness Results for a Nonlocal Bounbary Value Problem of Caputo-type Hadamard Hybrid Fractional Integro-differential Equations

This article is dedicated to study the existence and uniqueness of solutions for a non local bounbary value problem of Caputo-type Hadamard hybrid fractional integro-differential equations in Banach space, the recent researches considered the study of differential equations of Caputo-type Hadamard hybrid fractional integro-differential equations with classical order and the study of existence and uniqueness of solutions using approched numerical methodes, the objective of this paper is the study of the existence and uniqueness of fractional order of integro-differential equations involving the Caputo-type Hadamard derivative using fixed point theory. This work have two important results, the first result was the discussion of a new results owing to the fixed point theorem. Before the prove of results the problem was trandformed to Hadamard type problem. The first result based on Dhage fixed point theorem, after transforming our nonlocal boundary value problem into integral equation we defined operator equation, then we applied the fixed point theorem to get the existence resutl. The second result was the existence and uniqueness of solution for our nonlocal boundary value problem, we get this result using the Banach fixed point theorem. We illustrate our results by example to ending our theorical study.