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

In this paper, we are motivatedto evaluate and investigate the necessary conditions for the fractionalVolterra Fredholm integro-differential equation involving the $\varsigma $%-Hilfer fractional derivative. The given problem is converted into anequivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence anduniqueness results for the given problem are derived by applyingKrasnoselskii and Banach fixed point theorems respectively. Furthermore, weinvestigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.