Numerical Solution of System of Linear Fractional Integro-differential Equations by Least Squares Collocation Chebyshev Technique

Document Type : Original Article

Authors

1 Department of Applied Science, Faculty of Pure and Applied Science,Federal College of Dental Technology and Therapy, Enugu, Nigerian

2 Department of Mathematics, University of Ilorin, Ilorin, Nigerian

3 Department of Mathematics, America University of Nigerian

4 Department of Physical Sciences, Al-Hihmah University, Ilorin, Nigerian

5 Department of Mathematics, Modibbo Adama University, Yola, Nigerian

Abstract

This study presents the approximate solutions of a system of Fractional Integro-Differential Equations (FIDEs) with least squares collocation Chebyshev technique. The technique reduce the problem to system of linear algebraic equations and then solved. The applicability of this method has been demonstrated by numerical examples. Numerical results show that the method is easy to implement and compares favorably with the exact results.

Keywords


[1] L. Adam, Fractional Calculus: history, Definition and application for the engineer, Department of Aerospace and Mechanical Engineering University of Notre Dame, IN 46556, U.S.A., 2004.
[2] S. Alkan, V.F. Hatipoglu, Approximate solutions of Volterra- Fredholm integro-differential Equations of fractional order, Tbilisi Mathematical Journal, 10 (2) 2017, 1-13.
[3] Y.A. Amr, M. S. Mahdy, E. S. M Youssef, Solving fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method, Computers, Materials and Continua, 54 (2) 2018, 161-180.
[4] R. B. Adeniyi, On Tau method for the Numerical solution of ordinary differential equation, Ph.D. Thesis, University of Ilorin, Ilorin, Nigeria, 1991.
[5] D. Aysegul , V. B. Dilek, Solving fractional Fredholm integro-differential equations by Laguerre polynomials, Sains Malaysiana, 48(1) 2019, 251-257.
[6] F. Awawdeh, E.A. Rawashdeh, H.M. Jaradat, Analytic solution of fractional integro-differential Equations, Annals of the University of Craiova-Mathematics and Computer Science Series, 38 (1), 2011, 1-10.
[7] M. Caputo, Linear models of dissipation whose Q is almost frequency Independent, Geophysical Journal International, 13 (5) 1967, 529 –539.
[8] V. B. Dilkel, D. Aysegül, Applied collocation method using Laguerre polynomials as the basis Functions, Advances in difference equations a Springer Open Journal, 2018, 1-11.
[9] C. Edwards, Math 312 Fractional calculus final presentation, Accessed 20 Sep. 2018.
[10] X. Ma, C. Huang, Numerical solution of fractional integro- differential equations by a Hybrid collocation method, Applied Mathematics and Computation , 219 (12) 2013, 6750–6760.
[11] X. Ma, C. Huang, Spectral collocation method for linear fractional integro- differential Equations, Applied Mathematical Modelling, 38 (4) 2014, 1434-144.
[12] A. M. S. Mahdy, R. 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 (24) 2016, 24-32.
[13] D. Sh. Mohammed, Numerical solution of fractional integro- differential equations by least squares method and shifted Chebyshev polynomial, Mathematical Problems in Engineering, Article ID 431965, (1) 2014.
[14] D. Sh. Mohammed, Numerical solution of fractional singular integro-differential equations by using Taylor series expansion and Galerkin method, Journal of Pure and Applied Mathematics: Advances and Applications, 12 (2) 2014, 129-143.
[15] S. Nemati, S. Sedaghatb, I. Mohammadi, A fast numerical algorithm based on the second Kind Chebyshev polynomials for fractional integro-differential equations with weakly singular Kernels, Journal of Computational and Applied Mathematics, 308, 2016, 231-242.
[16] T. Oyedepo, A. F. Adebisi, M. T. Raji, M. O. Ajisope, J. A. Adedeji, J. O. Lawal, O. A. Uwaheren, Bernstein modified Homotopy perturbation method for the solution of Volterra Fractional integro- differential equations, Pasifi Journal of Science and Technology, 22(1) 2021, 30-36.
[17] H.M. Osama, A. A. Sarmad, Approximate solution of Fractional integro- differential equations by using Bernstein polynomials, Engineering and Technology Journal, 30 (8) 2012, 1362-1373.
[18] M.H. Saleh, S. H. Mohamed, M. H. Ahmed, and M. K. Marjan, System of linear fractional integro-differential equations by using Adomian decomposition method, International Journal of Computer Applications, 121 (24) 2015, 9–19.
[19] A. Setia, Y. Liu, A. S. Vatsala, Numerical solution of Fredholm- Volterra Fractional integro- differential equation with nonlocal boundary conditions”, Journal of Fractional Calculus and Applications, 5 (2) 2014, 155-165.
[20] O.A. Taiwo, Collocation approximation for singularly perturbed boundary value problems, Ph.D. Thesis, University of Ilorin, Nigeria, 1991.
[21] M. Yi, J. Huang, CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel, International Journal of Computer Mathematics, 92(8), 2015, 1715-1728.
Volume 3, Issue 2
May 2022
Pages 10-21
  • Receive Date: 20 November 2021
  • Revise Date: 23 April 2022
  • Accept Date: 26 April 2022
  • First Publish Date: 01 May 2022