Double-series expansion of the LRF method for fast-converging solutions of higher-order fractional PDEs with classical initial conditions

A new iterative analytic solution method of fractional linear partial differential equations with classical constraint conditions is developed. The method is based on a formula using generalized Taylor series, and a double fractional power series expansion has been used to provide a fast rate of convergence with little computational effort. It has been suggested as an alternative method to solve fractional-order differential equations that are common in engineering and physics. To validate the accuracy, potential, and applicability of the technique, some numerical test cases have been analyzed. Its efficiency and reliability have been proven by graphical and numerical results.