EXISTENCE AND APPROXIMATE SOLUTION FOR THE FRACTIONAL VOLTERRA FREDHOLM INTEGRO-DIFFERENTIAL EQUATION INVOLVING ζ-HILFER FRACTIONAL DERIVATIVE

Abstract

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ζ-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem ath and. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modiffed Adomian decomposition method. An example is provided to illustrate our findings