Computational Algorithm for Approximating Fractional Derivatives of Functions

John Ojima Mamman

doi:10.21467/jmsm.5.1.31-38

Authors

John Ojima Mamman Department of Mathematics/Statistics/Computer Science, Faculty of Science, Federal University of Agriculture Makurdi https://orcid.org/0000-0002-8373-328X

DOI:

https://doi.org/10.21467/jmsm.5.1.31-38

Abstract

This paper presents an algorithmic approach for numerically solving Caputo fractional diﬀerentiation. The trapezoidal rule was modiﬁed, the new modiﬁcation was used to derive an algorithm to approximate fractional derivatives of order α > 0, the fractional derivative used was based on Caputo deﬁnition for a given function by a weighted sum of function and its ordinary derivatives values at speciﬁed points. The trapezoidal rule was used in conjunction with the finite difference scheme which is the forward, backward and central difference to derive the computational algorithm for the numerical approximation of Caputo fractional derivative for evaluating functions of fractional order. The study was conducted through some illustrative examples and analysis of error.

Keywords:

Fractional Calculus, Finite difference Scheme, Modiﬁed trapezoidal rule

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