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A Green’s Function Iterative Approach for the Solution of a Class of Fractional BVPs Arising in Physical Models
, S.A. Khuri, A. Sayfy
Published in Springer
2020
Volume: 6
   
Issue: 4
Abstract
The aim of this study is to present an alternative approach for the numerical solution of a wide class of fractional boundary value problems (FBVPs) that arise in various physical applications. Examples of such FBVP include but not limited to Bagley–Torvik, Riccati, Bratu, and Troesch’s problems that appear in applied mathematics and mechanics. The method is based on first constructing an integral operator that is given in terms of the Green’s function associated with the linear differential term of the fractional differential equation. Fixed point iterative procedures, such as Picard’s and Mann’s, are then applied to the operator to generate an iterative scheme that yields a convergent semi-analytical solution. Numerical examples are reported to confirm the efficiency, reliability, accuracy and fast convergence of the scheme. © 2020, Springer Nature India Private Limited.
About the journal
JournalData powered by TypesetInternational Journal of Applied and Computational Mathematics
PublisherData powered by TypesetSpringer
ISSN23495103