Leila Torkzadeh - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.
Somayyeh Dadsetadi - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.

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