Solving fractional differential equations numerically

Abstract

In this paper we present a brief review about fractional calculus and also the fractional Adam-Bashforth method for solving fractional differential equations. The fractional Adam-Bashforth method is due to Diethelm et al. [¹] and is characterized by its efficiency, as it considers the memory effects of fractional differentiation. The presentation is performed in a pedagogical perspective, delivered to beginner in the subject. In this context, some examples are presented and applications are discussed.

Keywords
Fractional Calculus; Caputo’s Derivative; Fractional Adam-Bashforth Method