ABSTRACT
Fractional calculus is an emerging and popular field among the science and engineering community. Many physical problems [156, 47, 44, 194] are modeled by fractional differential equations and fractional integral equations, and obtaining solutions of these equations have been the subject of many researchers in recent years. Frequently many researchers search lot of dynamical
oscillation of earthquakes, fluiddynamic traffic, frequency dependent damping behavior of many viscoelastic materials, continuum and statistical mechanics, solid mechanics, economics, signal processing, and control theory [26, 121, 165, 27, 111]. These fractional integral equations and integro-differential equations have been solved both analytically and numerically [74, 174, 177]. Many analytical methods like the Adomian decomposition method [141], the homotopy perturbation method [189], the homotopy analysis method [82], the variational iteration method [104], the fractional differential transform method (FDTM) [14], the generalized block pulse operational matrix method [16], and the Laplace transform method [156] have been developed to solve fractional integral equations and integro-differential equations. But the analytical solutions of fractional integral or integro-differential equations are not obtainable always. That is the main reason why finding the numerical solutions of these problems has become a great deal for many researchers.
