Computational Analysis Of Fractional Volterrafredholm Integro-Differential Equation Using Eulerian  Polynomial Basis Function

Authors

  • M. T. RAJI Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria Author
  • O. FAGBEMIRO Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria Author
  • B. I. OLAJUWON Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria Author

DOI:

https://doi.org/10.60787/jnamp.v68no1.430

Keywords:

Fractional, IntegroDifferential Equations(IDE’s), Eulerian, Polynomial, Lagrange

Abstract

This study develops a novel eulerian polynomial function for fractionallydifferentiated Linear Volterra-Fredholm Integro-differential equations (LVFIDEs). The procedure is developed and evaluated against the current set of Lagrange polynomials (LPs); In order to achieve the best results and implementation of these kinds, a general algorithm is recommended and examples are provided. Additionally, using MATLAB 2009 software, a special case fractional differential equation is used to assess the viability of the suggested approach. In order to assess how well the suggested strategy solves difficulties, comparisons between it and current approaches are finally provided.

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Author Biography

  • M. T. RAJI, Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria


    , FAGBEMIRO O. and OLAJUWON B. I.
    Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria

    *Corresponding author: RAJI M.T
    E-mail address: rajimt@funaab.edu.ng

References

Mittal R. C., Nigam R. Solution of Fractional IntegroDifferential Equations by Adomian Decomposition Method. Int. J. of Appl. Math. and Mech. 2008;4(2):87-94.

Mohammed D. S. H. Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial. Math. Probl. Eng. [Internet]. 2014; 2014(5):1-5. Available from: http://dx.doi.org/10.1155/2014/431965.

Huang L, Li X. F., Zhao Y, Duan X. Y. Approximate Solution of Fractional IntegroDifferential Equation by Taylor Expansion Method. Comput. Math Appl. [Internet] . 2011; 62: 1127-1134. Available from: https://doi.org/10.1016/j.camwa.2011.03.037.

Maleknejad K, Sahlan M. N, Ostadi A. Numerical Solution of Fractional Integrodifferential Equation by Using Cubic B-spline Wavelets. Proceedings of the World Congress of Engineering. 2013 July; I(WCE 2013) :3-8.

Mohamed M. S, Alharthi M. R, Alotabi R. A. Solving Fractional Integro-Differential Equation by Homotopy Analysis Transform Method. IJPAM. [Internet].2016;106(4): 1037-1055. Available from: http://www.ijpam.eu,doi:10.12732/ijpam.v106i4.6.

Shwayyea R. T, Mahdy A. M. S. Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Laguerre Polynomials Pseudo-Spectral Method. IJSER. 2016(April); 7(4):1589-1596.

Oyedepo T, Taiwo O. A., Abubakar J. U, Ogunwobi Z. O. Numerical studies for Solving Fractional IntegroDifferential Equations by using Least Squares Method and Bernstein Polynomials. Fluid Mech Open Acc. [Internet].2016; 3(3). Available from: http://DOI:10.4172/2476-2296.1000142.

Senol M, Kasmaei H. D. On the Numerical Solution of Nonlinear Fractional-Integro - Differential Equations. NTMSCI. 2017;5(3):118-127.

Alkan S, Hatipoglu V. F. Approximate Solution of Volterra-Fredholm Integro-Differential Equations of Fractional Order. TMJ.2017; 10 (2) :1-13.

Syam M. I. Analytical Solution of the Fractional Fredholm Integro Differential Equation using the Fractional Residual Power Series Method. Complexity. [Internet]. 2017;2017:1-6. Available from: https://doi.org/10.1155/2017/4573589.

Hamoud A. A, Ghadle K. P. Modified Laplace Decomposition Method for Fractional VolterraFredholm Integro-Differential Equation. JMM.2018; 6 (1):91-104.

Hamoud A. A, Ghadle K. P, Issa M. S. B, Giniswamy. Existence and Uniqueness Theorems for Fractional Volterra-Fredholm Integro-Differential Equations. IJAM. 2018; 31(3):333 -348.

Wang K, Wang Q. The Lagrange Collocation Method for Solving the Volterra– Fredholm Integral Equations. Appl Math Comput.2013; 219 (21): 10434-10440.

Mustafa M. M, Muhammad A. M. Numerical Solution of Linear Volterra-Fredholm Integro-Differential Equations Using Lagrange Polynomials. Theory Appl . 2014; 4(9): 158-166.

Mustafa M. M, Ghanim I. N. Numerical Solution of Linear Volterra-Fredholm Integra Equations Using Lagrange Polynomials. Theory Appl . 2014; 4(5): 137-146.

Liu H, Huang J, Pan Y. Numerical Solution of Two Dimensional Fredholm Integral Equations of the Second Kind by the Barycentric Lagrange Function. JAMP.2017; 5: 259-266.

Pan Y, Huang J. Numerical Solution of TwoDimensional Fredholm Integral Equations via Modification of Barycentric Rational Interpolation. Adv. Eng. Softw. 2017; 118(Amcce):582–586.

Tian D, He J. The Barycentric Rational Interpolation Collocation Method for Boundary Value Problems. THERM SCI.2018; 22 (4): 1773-1779.

Wu H, Wang Y. Zhang W. Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method. Math. Probl. Eng. [Internet] . 2018; 2018, Available from: https://doi.org/10.1155/2018/7260346.

Salman N. K. and Mustafa, M. M. Numerical solution of Fractional VolterraFredholm Integro-Differential Equation Using Lagrange Polynomials. Baghdad Science Journal 2020: 17 (4): 1234 – 1240 Available from: http://dx.doi.org/10.21123/bsj.2020:17.4.1234.

Elbeleze, A. A, Kilicman, A, Taib, B. M. Approximate solution of IntegroDifferential equation of fractional (arbitrary) order. Journal of King Saud UniversityScience. 2015; 1-8. Available from http://dx.doi.org/10.10.16/j.jksus.2015.04.006

Oraekie, P. A. Null controllability of fractional Integro-Differential systems in Banach spaces with distributed delays in the limited control powers. Journal of the Nigerian Association of Mathematical Physics; 2018; 48: 1-10

Hirzebtuch, F. Eulerian polynomials Munster J. of Math. 1 2008, 9 – 14.

Mathews J. H, Fink K. D. Numerical Methods Using MATLAB. 3rd Edition, Prentice Hall, Inc.1999.662p 21.Berrut J. P, Trefethen L. N. Barycentric Lagrange Interpolation. SIAM REV..2004; 46(3): 501-517.

Higham N. J. The Numerical Stability of Barycentric Lagrange Interpolation IMA J. Numer. Anal.2004;24(4): 547–556.

Daşcioğlu A, Bayram D. V. Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials. Sains Malays. 2019; 48(1):251-257.

Odibat Z. M, Momani S. H. An Algorithm for the Numerical Solution of Differential Equations of Fractional Order", JAMSI .2008; 26(1-2): 15-27.

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Published

2024-10-23

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How to Cite

Computational Analysis Of Fractional Volterrafredholm Integro-Differential Equation Using Eulerian  Polynomial Basis Function. (2024). The Journals of the Nigerian Association of Mathematical Physics, 68, 141-150. https://doi.org/10.60787/jnamp.v68no1.430

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