Numerical Solution of Fractional Volterra-Fredholm Integro-Differential Equation Using Lagrange Polynomials

Main Article Content

Nour Salman
https://orcid.org/0000-0001-7786-1851
Muna Mansour Mustfaf
https://orcid.org/0000-0001-8620-4976

Abstract

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal method in solving these problems.

Article Details

How to Cite
1.
Numerical Solution of Fractional Volterra-Fredholm Integro-Differential Equation Using Lagrange Polynomials. Baghdad Sci.J [Internet]. 2020 Dec. 1 [cited 2024 Mar. 28];17(4):1234. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3389
Section
article

How to Cite

1.
Numerical Solution of Fractional Volterra-Fredholm Integro-Differential Equation Using Lagrange Polynomials. Baghdad Sci.J [Internet]. 2020 Dec. 1 [cited 2024 Mar. 28];17(4):1234. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3389

References

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

Mohammed D Sh. 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 XF, Zhao Y, Duan XY. Approximate Solution of Fractional Integro-Differential 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 MN, Ostadi A. Numerical Solution of Fractional Integro-differential Equation by Using Cubic B-splin Wavelets. Proceedings of the World Congress of Egeineering. 2013 July; I(WCE 2013) :3-8.

Mohamed MS, Alharthi MR, Alotabi RA. 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 RT, Mahdy AMS. 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 OA, Abubakar JU, Ogunwobi ZO. Numerical studies for Solving Fractional Integro-Differential Equations by using Least Squares Method and Bernstein Polynomials. Fluid Mech Open Acc. [Internet].2016; 3(3). Available from: DOI:10.4172/2476-2296.1000142.

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

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

Syam MI. 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 AA, Ghadle KP. Modified Laplace Decomposition Method for Fractional Volterra-Fredholm Integro-Differential Equation. JMM.2018;6(1):91-104.

Hamoud AA, Ghadle KP, Issa MSB, 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 MM, Muhammad AM. Numerical Solution of Linear Volterra-Fredholm Integro-Differential Equations Using Lagrange Polynomials. Theory Appl . 2014; 4(9): 158-166.

Mustafa MM, Ghanim IN. Numerical Solution of Linear Volterra-Fredholm Integral 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 Two-Dimensional 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.

Mathews JH, Fink kD. Numerical Methods Using MATLAB. 3rd Edition, Prentice Hall, Inc.1999.662p

Berrut JP, Trefethen LN. Barycentric Lagrange Interpolation. SIAM REV..2004; 46(3): 501-517.

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

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

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

Similar Articles

You may also start an advanced similarity search for this article.