Md Habibur Rahman, Muhammad I Bhatti* and Nicholas Dimakis

University of Texas Rio Grande Valley, Edinburg, Texas, USA

*Corresponding Author: Muhammad I Bhatti, University of Texas Rio Grande Valley, Edinburg, Texas, USA.

Received: September 27, 2022; Published: October 31, 2022

Abstract

>In this article, the fractional Bhatti-Polynomial bases are applied to solve one-dimensional nonlinear fractional differential equations (NFDEs). We derive a semi-analytical solution from a matrix equation using an operational matrix which is constructed from the terms of the NFDE using Caputo's fractional derivative of fractional B-polynomials (B-polys). The results obtained using the prescribed method agree well with the analytical and numerical solutions presented by other authors. The legitimacy of this method is demonstrated by using it to calculate the approximate solutions to four NFDEs. The estimated solutions to the differential equations have also been compared with other known numerical and exact solutions. It is also noted that for solving the NFDEs, the present method provides a higher order of precision compared to the various finite difference methods. The current technique could be effortlessly extended to solving complex linear, nonlinear, partial, and fractional differential equations in multivariable problems.

Keywords: Fractional B-Polynomials; Fractional Differential Equations; Nonlinear Partial Fractional Differential Equation; FRACTIONAL B-polynomials in Multiple Variables

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Citation

Citation: Muhammad I Bhatti., et al. “A Method to Solve One-dimensional Nonlinear Fractional Differential Equation Using B-Polynomials". Acta Scientific Applied Physics 2.11 (2022): 22-35.

Copyright

Copyright: © 2022 Muhammad I Bhatti., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.