"Approximate Scheme for Fractional Differential Equation of Order 1 < α" by Dhrumit K. Trivedi and Nimisha Pathak

Progress in Fractional Differentiation & Applications

Article Title

Approximate Scheme for Fractional Differential Equation of Order 1 < α < 2 Using Finite Difference Method

Authors

Dhrumit K. Trivedi, Department of Applied Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, IndiaFollow
Nimisha Pathak, Department of Applied Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, IndiaFollow

Author Country (or Countries)

India

Abstract

In this article, we develop composite Simpson’s ( 1 /3) rd rule for fractional differential equation with Caputo derivative of order α, 1<α < 2 using finite difference method. We use forward, central and backward difference formulae for approximating the derivatives. We give comparison of numerical solution given by Simpson’s ( 1 )rd rule and Trapezoidal rule. Result shows that Simpson’s rule gives better approximation. Furthermore, as an application of the scheme we solve test problems using Mathematical software.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090307

Recommended Citation

K. Trivedi, Dhrumit and Pathak, Nimisha (2023) "Approximate Scheme for Fractional Differential Equation of Order 1 < α < 2 Using Finite Difference Method," Progress in Fractional Differentiation & Applications: Vol. 9: Iss. 3, Article 7.
DOI: http://dx.doi.org/10.18576/pfda/090307
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol9/iss3/7

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