A Numerical Scheme for Solving Nonlinear Boundary Value Problems of Fractional Order 0 ≤ β ≤ α < 1 | [Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences • 2018]

Author(s):

1. Muhammad Adnan Anwar: Department of Mathematics, University of Engineering and Technology,Lahore,Pakistan

2. Shafiq Ur Rehman: Department of Mathematics, University of Engineering and Technology,Lahore,Pakistan

3. Fayyaz Ahmad: Department de Fisica i Enginyeria Nuclear, Universitat Polite`cnica de Catalunya,Eduard Maristany 10, Barcelona,

Abstract:

The primary objective of this research work is to find accurate numerical approximations for nonlinear fractional order boundary value problems (BVPs). To carry out this goal, central finite difference scheme of order four is used to approximate first- and second-order derivatives. Integrals are approximated using composite Trapezoidal rule in “the Caputo definition”. The effectiveness of the proposed scheme is illustrated by solving nonlinear fractional order BVPs of order 0 = ß = a < 1.

Page(s): 59-69

DOI: DOI not available

Published: Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 55, Issue: 4, Year: 2018

Keywords:

Trapezoidal rule , Boundary value problems , Fractional differential equations , Central finite difference scheme

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