Existence and uniqueness of integrable solutions of fractional order initial value equations

Document Type : Research Article


1 Department of Mathematics, Poona College of Arts, Science and Commerce, Camp, Pune, India & Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia

2 Department of Mathematics, Pratishthan Mahavidyalaya, Paithan, Aurangabad, India


This paper is devoted to investigate some  existence and uniqueness results of integrable solutions for nonlinear  fractional order initial value differential equations  involving Caputo operator. We develop  the existence of integral solution using Schauder's fixed point theorem. In addition, by applying the Banach contraction principle, we establish  uniqueness result. To illustrate the applicability of main results, two examples are presented.