Exact Solutions of Second-order Fractional Fredholm Integro-differential Equations
Abdelhalim Ebaid *
Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk 71491, Saudi Arabia.
Ohoud A. Alshahrani
Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk 71491, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
The present paper analyzes the second-order fractional Fredholm integro-differential equations by means of the Caputo definition in the fractional calculus (FC). The exact solutions are obtained for two examples utilizing a direct solution method. Furthermore, it is shown that the present solutions in fractional forms reduce to the corresponding classical ones in the relevant literature, with integer derivatives, as special cases.
Keywords: Fractional integral equations, Fredholm, integro-differential equations, exact solution