Analytical and numerical techniques for solving a fractional integro-differential equation in complex space

In this article, we describe the existence and uniqueness of a solution to the nonlinear fractional Volterra integro differential equation in complex space using the fixed-point theory. We also examine the remarkably effective Euler wavelet method, which converts the model to a matrix structure that lines up with a system of algebraic linear equations; this method then provides approximate solutions for the given problem. The proposed technique demonstrates superior accuracy in numerical solutions when compared to the Euler wavelet method. Although we provide two cases of computational methods using MATLAB R2022b, which could be the final step in confirming the theoretical investigation.