Approximate Method for Solving System of Linear Fredholm Fractional Integro-Differential Equations Using Least Squares Method and Lauguerre Polynomials

Authors

DOI:

https://doi.org/10.26713/cma.v14i1.2007

Keywords:

System of linear Fredholm fractional integro-differential equations, Least square method, Lauguerre polynomials, Caputo derivative

Abstract

An attempt is made to develop approximate method to get approximate solution of system of linear Fredholm fractional integro-differential equations using Least squares and Lauguerre polynomial method. The system of linear Fredholm fractional integro-differential equations is reduced to a system of linear equations using Lauguerre polynomials. The method is implemented to obtain approximate solution of the system of Fredholm fractional integro-differential equations. The solutions are simulated using Scilab.

Downloads

Download data is not yet available.

References

W. W. Bell, Special Functions for Scientists and Engineers, D. van Norstrand Company, London (1968).

M. Didgar, A. R. Vahidi and J. Biazar, An approximate approach for systems of fractional integro-differential equations based on Taylor expansion, Kragujevac Journal of Mathematics 44(3) (2020), 379 – 392, DOI: 10.46793/KgJMat2003.379D.

A. M. S. Mahdy and E. M. H. Mohamed, Numerical studies for solving system of linear fractional integro-differential equations by using least squares method and shifted Chebyshev polynomials, Journal of Abstract and Computational Mathematics 1(1) (2016), 24 – 32, URL: https://www.ntmsci.com/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=7185.

A. M. S. Mahdy, Numerical studies for solving fractional integro-differential equations, Journal of Ocean Engineering and Science 3(2) (2018), 127 – 132, DOI: 10.1016/j.joes.2018.05.004.

S. Momani and R. Qaralleh, An efficient method for solving systems of fractional integro-differential equations, Computers & Mathematics with Applications 52(3-4) (2006), 459 – 470, DOI: 10.1016/j.camwa.2006.02.011.

J. A. Nanware, P. M. Goud and T. L. Holambe, Solution of fractional integro-differential equations by Bernstein polynomials, Malaya Journal of Matematik S1 (2020), 581–586, DOI: 10.26637/MJM0S20/0111.

J. A. Nanware, P. M. Goud and T. L. Holambe, Numerical solution of fractional integro-differential equations using Hermite polynomials, Journal of Mathematical and Computational Science 11(6) (2021), 8448 – 8457, DOI: 10.28919/jmcs/6633.

I. Podlubny (editor), Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications, Mathematics in Science and Engineering series, Vol. 198, Academic Press, San Diego – California, USA, 340 pages (1999), URL: https://www.sciencedirect.com/bookseries/mathematics-in-science-and-engineering/vol/198/suppl/C.

R. K. Saeed and H. M. Sdeq, Solving a system of linear fredholm fractional integro-differential equations using homotopy perturbation method, Australian Journal of Basic and Applied Sciences 4(4) (2010), 633 – 638.

H. A. Zedan, S. S. Tantawy and Y. M. Sayed, New solutions for system of fractional integro-differential equations and Abel’s integral equations by Chebyshev spectral method, Mathematical Problems in Engineering 2017 (2017), Article ID 7853839, DOI: 10.1155/2017/7853839.

M. Zurigat, S. Momani and A. Alawneh, Homotopy analysis method for systems of fractional integro-differential equations, Neural, Parallel and Scientific Computations 17(2) (2009), 169 – 186, URL: https://www.dynamicpublishers.com/Neural/NPSC2009/11-NPSC-09-FINAL.pdf.

Downloads

Published

09-05-2023
CITATION

How to Cite

Goud, P. M., Nanware, J. A., Holambe, T. L., & Jadhav, N. B. (2023). Approximate Method for Solving System of Linear Fredholm Fractional Integro-Differential Equations Using Least Squares Method and Lauguerre Polynomials. Communications in Mathematics and Applications, 14(1), 459–470. https://doi.org/10.26713/cma.v14i1.2007

Issue

Section

Research Article