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Employing A Fractional Basis Set To Solve Nonlinear Multidimensional Fractional Differential Equations, Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis

Physics and Astronomy Faculty Publications and Presentations

Fractional-order partial differential equations have gained significant attention due to their wide range of applications in various fields. This paper employed a novel technique for solving nonlinear multidimensional fractional differential equations by means of a modified version of the Bernstein polynomials called the Bhatti-fractional polynomials basis set. The method involved approximating the desired solution and treated the resulting equation as a matrix equation. All fractional derivatives are considered in the Caputo sense. The resulting operational matrix was inverted, and the desired solution was obtained. The effectiveness of the method was demonstrated by solving two specific types of nonlinear multidimensional fractional …