An enhanced hybrid fractional order modified Taylor wavelets Galerkin approach for the numerical simulation of fractal-fractional integro-differential equations

The main focus of this study is to provide a complete discretization approach for solving Volterra and Fredholm integro-differential equations of second kind by incorporating modified Taylor wavelets of fractional order under the Riemann–Liouville fractal-fractional derivative. Firstly, the unknown function is approximated by employing fractional order modified Taylor wavelets and then the considered model is reduced into a set of algebraic equations leveraging the Galerkin method. The key purpose of this paper is to determine the efficiency, accuracy and reliability of the proposed approach through theoretical study and numerical examples. The validity of the suggested method is shown through tables where the absolute errors are compared with other existing techniques. For various fractal-fractional values of different model parameters, the residual errors are examined which constantly minimized by simply increasing the number of wavelet basis. Moreover, the graphs clearly depict that the approximate solutions coincide with the analytical solution.