CATALAN COLLOCATIONS TAU METHOD FOR SOLUTION OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

Authors

  • Musa Isiyaku
    Modibbo Adama University
  • Jerry Amos
    Adamawa State College of Education
  • Adebayo S. Oladoja
    Modibbo Adama University
  • Y. B. Chukkol
    Modibbo Adama University
  • Bala M. Jingi
    Adamawa State College of Education

Keywords:

Collocation Tau Method, Fractional Fredholm Integro-differential Equations, Fractional derivatives

Abstract

This article is concern with the numerical solution of Fractional order Fredholm Integro-differential Equations using Catalan tau collocation method. The concept of Catalan tau collocation method was implemented on some of fractional Fredholm integro-differential equations to illustrate the efficienciency and practicability of the method. Fractional derivatives in Riemann-Liouvilles sense were adopted throughout this article.. The results showed the reliable, efficacy and accuracy that the method exhibited for this kind of problems when compared to the analytic solutions.

Dimensions

Abou-Hayt, I., & Dahl, B. (2023). A Critical Look at the Laplace Transform Method in Engineering Education. IEEE Transactions on Education, 67(4), 542-549.

Ali, K. K., Abd El Salam, M. A., Mohamed, E. M., Samet, B., Kumar, S., & Osman, M. S. (2020). Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series. Advances in Difference Equations, 2020, 1-23.

Bozyigit, B. (2021). Seismic response of pile supported frames using the combination of dynamic stiffness approach and Galerkin’s method. Engineering Structures, 244, 112822.

Çevik, M., Savaşaneril, N. B., & Sezer, M. (2025). A Review of Polynomial Matrix Collocation Methods in Engineering and Scientific Applications. Archives of Computational Methods in Engineering, 1-19.

Fakhar‐Izadi, F., & Dehghan, M. (2013). An efficient pseudo‐spectral Legendre–Galerkin method for solving a nonlinear partial integro‐differential equation arising in population dynamics. Mathematical Methods in the Applied Sciences, 36(12), 1485-1511.

Fathy, M. (2021, December). Legendre-Galerkin method for the nonlinear Volterra-Fredholm integro-differential equations. In Journal of Physics: Conference Series (Vol. 2128, No. 1, p. 012036). IOP Publishing.

García-Vidal, G., Pérez-Campdesuñer, R., Sánchez-Rodríguez, A., & Martínez-Vivar, R. (2019). Chain substitution and successive approximation method: Throughput analysis at SMEs. International Journal of Engineering Business Management, 11, 1847979019838397.

Guled, C. N., Tawade, J. V., Kumam, P., Noeiaghdam, S., Maharudrappa, I., Chithra, S. M., & Govindan, V. (2023). The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method. Results in Engineering, 18, 101173.

Herrera, I., Yates, R., & Rubio, E. (2007). Collocation methods: More efficient procedures for applying collocation. Advances in Engineering Software, 38(10), 657-667.

Iweobodo, D. C., Njoseh, I. N., & Apanapudor, J. S. (2023). A new wavelet-based galerkin method of weighted residual function for the numerical solution of one-dimensional differential equations. Mathematics and statistics, 11(6), 910-916.

Jiang, W., & Gao, X. (2024). Review of Collocation Methods and Applications in Solving Science and Engineering Problems. CMES-Computer Modeling in Engineering & Sciences, 140(1).

Kim, D. S., & Kim, T. (2017). A new approach to Catalan numbers using differential equations. Russian Journal of Mathematical Physics, 24(4), 465-475.

Mahdy, A. M., & Mohamed, E. M. (2016). 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(24), 24-32.

Mahdy, A. M. S., Mohamed, E. M. H., & Marai, G. M. A. (2016). Numerical solution of fractional integro-differential equations by least squares method and shifted Chebyshev polynomials of the third kind method. Theoretical Mathematics & Applications, 6(4), 87-101.

Mamadu, J. E., & Njoseh, I. N. (2016). Tau-collocation approximation approach for Solving first and second order ordinary differential equations. Journal of Applied Mathematics and Physics, 4(2), 383-390.

Mokhtary, P. (2016). Discrete Galerkin method for fractional integro-differential equations. Acta Mathematica Scientia, 36(2), 560-578.

Mostafa, M., AM A, H., Abbas, W., & Fathy, M. (2021). Galerkin method for nonlinear Volterra-Fredholm integro-differential equations based on Chebyshev polynomials. Engineering Research Journal, 170, 169-183.

Odekunle, M. R. (2006). Catalan collocation Tau method of solution of ordinary defferential quations. Global Journal of Mathematical Sciences, 5(2), 105-110.

Oyedepo, T., Ayoade, A., Ajileye, G., & Ikechukwu, N. J. (2023). Legendre computational algorithm for linear integro-differential equations. Cumhuriyet Science Journal, 44(3), 561-566.

Shahmorad, S. (2005). Numerical solution of the general form linear Fredholm–Volterra integro-differential equations by the Tau method with an error estimation. Applied Mathematics and Computation, 167(2), 1418-1429.

Tomar, S., Singh, M., Vajravelu, K., & Ramos, H. (2023). Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier. Mathematics and Computers in Simulation, 204, 640-644.

Turkyilmazoglu, M. (2019). Accelerating the convergence of Adomian decomposition method (ADM). Journal of Computational Science, 31, 54-59.

Ullah, S., Amin, F., & Ali, M. (2024). Numerical Investigation with Convergence and Stability Analyses of Integro-Differential Equations of Second Kind. International Journal of Computational Methods, 21(03), 2350036.

Uwaheren, O. A., Adebisi, A. F., & Taiwo, O. A. (2020). Perturbed collocation method for solving singular multi-order fractional differential equations of Lane-Emden type. Journal of the Nigerian Society of Physical Sciences, 141-148.

Wohlmuth, B. I. (2012). Discretization methods and iterative solvers based on domain decomposition (Vol. 17). Springer Science & Business Media.

Zayernouri, M., & Karniadakis, G. E. (2014). Fractional spectral collocation method. SIAM Journal on Scientific Computing, 36(1), A40-A62.

Published

26-09-2025

How to Cite

CATALAN COLLOCATIONS TAU METHOD FOR SOLUTION OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. (2025). FUDMA JOURNAL OF SCIENCES, 9(9), 312-316. https://doi.org/10.33003/fjs-2025-0909-3791

Issue

Vol. 9 No. 9 (2025): FUDMA Journal of Sciences - Vol. 9 No. 9

Section

Research Articles
Copyright & Licensing

Copyright (c) 2025 Musa Isiyaku, Jerry Amos, Adebayo S. Oladoja, Y. B. Chukkol, Bala M. Jingi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

CATALAN COLLOCATIONS TAU METHOD FOR SOLUTION OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS. (2025). FUDMA JOURNAL OF SCIENCES, 9(9), 312-316. https://doi.org/10.33003/fjs-2025-0909-3791