Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 7 1 2022 11 01 Conformity of Fractional Volterra Integro-Differential Equation Solution with an Integral Equation of Fractional Order 101 108 288 10.22128/gadm.2022.587.1077 EN Leila Torkzadeh Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran. 0000-0002-2504-4048 Somayyeh Dadsetadi Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran. Journal Article 2022 08 20 For the feasibility of using analytical and numerical studies and findings on fractional integral equations for integro-differential of the fractional order, in this work, the equivalence of a fractional Volterra integro-differential equation of the Hammerstein type with a fractional integral equation is investigated in the Banach space. For this purpose, we use the mutual properties of the fractional order derivative and integral on each other. Fractional integro-differential equation Hammerstein equation Riemann-Liouville fractional integral Caputo derivative https://ansne.du.ac.ir/article_288_ec051a1b021c92ce61a1beb32d972061.pdf