Exploring applications of fractional differential equations with radial basis function

Abstract

Solving fractional order differential equations is substantially more complex than solving ordinary order differential equations; also, the majority of computing tools do not include built-in functions for this type of issue. In this article, we establish the fundamentals of fractional order differential equations such as Riemann-Liouville, Caputo, Riesz fractional, etc. Also, we provide a brief overview of the fundamental techniques for solving linear fractional differential equations. Due to diverse applications in solving various models based on fractional-order differential equations, the invention and exploration of numerical methods to find their solutions. Radial basis function methods are one of such methods to find the more accurate and convergent solutions compared to the other methods.