Vieta-Lucas Spectral Collocation Method for Solving Fractional Order Volterra Integro-differential Equations.


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Authors

  • Mustafa Khirallah Ibb Univeristy,Ibb ,yemen

Keywords:

fractional order Volterra integro-differential equations;, Caputo type fractional derivative;, Vieta-Lucas spectral collocation method;, Residual error function

Abstract

The shifted Vieta-Lucas polynomial approach is taken into account for the numerical solution of linear and nonlinear fractional-order integro-differential equations of the Volterra type. Fractional derivatives are described in the Caputo sense. The suggested method reduces the complexity of these problems to the linear or nonlinear solution of algebraic equations. The convergence of the recommended strategy is studied in detail. The computing efficiency of this approach is then  illustrated with certain numerical examples, and a comparison with prior research is made.

 

References

I. Podlubny, Fractional Differential Equations Academic Press, San Diego, 1999.

K. 8. Miller; B;, Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations; Wiley: Hoboken, NJ, USA, 1993 Equations Academic Press, San Diego, 1999.

S. G. Kilbas, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications Gordon & Breach, Yverdon 1993.

M. D. Johansyah, A. K. Supriatna, E. Rusyaman, J. Saputra Application of fractional differential equation in economic growth model: A systematic review approach[J]. J. Econom. 6(9),10266-10280, 2021

D. Kumar, J. Singh, Fractional Calculus in Medical and Health Science, CRC Press, 2021.

F. Zhu, et al. Physics-motivated fractional viscoelasticity model for dynamic relaxation in amorphous solids, International Journal of Plasticity 164, 103588, 2023.

Y. A. Rossikhin, M. V. Shitikova, Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids, Appl. Mech. Rev. , 50, 15-67, 1997.

A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. In North-Holland Mathematics Studies; Elsevier: Amsterdam, The Netherlands, 2006; Volume 204

Diethelm, K. An algorithm for the numerical solution of differential equations of fractional order. Electron. Trans. Numer. Anal. 1997, 5, 1-6.

M. Alghtani, M. M. Khader, K. M. Saad, Numerical simulation for a high-dimensional chaotic Lorenz system based on Gegenbauer wavelet polynomials, Mathematics, 2023 11(2), 472

H. M. Srivastava, K. M. Saad, W. M. Hamanah, Certain new models of the multi-space fractal-fractional Kuramoto-Sivashinsky and Korteweg-de Vries equations, Mathematics, 2023 10(7), 1089

Abd-Elhameed, W.M.; Youssri, Y.H., Connection formulae between generalized Lucas polynomials and some Jacobi polynomials: Application to certain types of fourth-order BVPs.Int. J. Appl. Comput. Math. 2020, 6, 1-19.

Agarwal, F.; El-Sayed, A.A. Vieta-Lucas polynomials for solving a fractional-order mathematical physics model. Adv. Differ. Equ. 2020, 2020, 1-18.

Horadam, A.F. Vieta Polynomials The University of New England, Armidaie, Australia 2000.

Zakaria, M.; Khader, M.M.; Ibrahim Al-Dayel; Al-Tayeb, W. Solving fractional generalized Fisher-Kolmogorov-Petrovsky-Piskunov’s equation using compact finite different method to gether with spectral collocation algorithms. Journal of Mathematics (2022), 15, 1-12.

A. Constantinides, Applied numerical methods with personal computers (McGraw-Hill, New York, 1987).

A. Arikoglu and I. Ozkol, “Solution of fractional integro-differential equations by using fractional differential transform method”, Chaos Solitons Fractals (2009),34, 521-529.

Q. Wu, Z. Wu, X. Zeng, A Jacobi Spectral Collocation Method for Solving Fractional Integro-Differential Equations. Commun. Appl. Math. Comput. 2021, 3,509-526.

N. Rajagopal , S. Balaji , R. Seethalakshmi , V.S. Balaji, A new numerical method for fractional order Volterra integro-differential equations, Ain Shams Engineering Journal, 2020 11, 171-177

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Published

2023-12-02

How to Cite

Khirallah, M. (2023). Vieta-Lucas Spectral Collocation Method for Solving Fractional Order Volterra Integro-differential Equations. Results in Nonlinear Analysis, 7(1), 14–23. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/302