%0 Journal Article %T Existence and uniqueness of integrable solutions of fractional order initial value equations %J Journal of Mathematical Modeling %I University of Guilan %Z 2345-394X %A Sontakke, Bhausaheb %A Shaikh, Amjad %A Nisar, Kottakkaran %D 2018 %\ 12/01/2018 %V 6 %N 2 %P 137-148 %! Existence and uniqueness of integrable solutions of fractional order initial value equations %K Integrable solution %K existence and uniqueness %K Caputo operator %K fixed point theorems %R 10.22124/jmm.2018.9971.1147 %X 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. %U https://jmm.guilan.ac.ir/article_2917_bfcae2cf130e3ebe53c6bccd3a6b54d6.pdf