Solving Fractional Delay Integro-Differential Equations by Chebyshev Wavelets

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-7
Year of Publication : 2021
Authors : S. C. Shiralashetti, B. S. Hoogar


MLA Style: S. C. Shiralashetti, B. S. Hoogar "Solving Fractional Delay Integro-Differential Equations by Chebyshev Wavelets" International Journal of Mathematics Trends and Technology 67.7 (2021):158-168. 

APA Style: S. C. Shiralashetti, B. S. Hoogar(2021). Solving Fractional Delay Integro-Differential Equations by Chebyshev Wavelets International Journal of Mathematics Trends and Technology, 158-168.

In this article, an efficient numerical technique based on second kind Chebyshev wavelets is proposed to solve a class of fractional delay integro-differential equations. The operational matrix of fractional integration is used to convert the equation under investigation into a system of algebraic equations which can be solved easily. Illustrative examples are included to demonstrate the high accuracy and applicability of the method. In addition, the numerical results are compared with exact solutions and other existing methods confirm that present technique is more efficient.


[1] Igor Podlubny, Fractional differential equations, Academic press, San Diego. (1999).
[2] W.H. Deng, C.P. Li, Chaos Synchronization of the fractional Lii System, Physica A. 39(2) (2005) 61-72.
[3] E.Baskin, A.Iomin, Electro Chemical manifestation of nanoplasmonics in fractal media,Open phys. 11(6) (2013) 676-684 .
[4] T.T. Hartley, C.F.Lorenzo, H.K., Qammer, Chaos in a fractional order Chua’s system, IEEE Trans. Circuits Syst. I Fundam. Theory Appl, 42(8) (1995) 485-490.
[5] A.A.Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier science. 204 (2006) 540-565.
[6] M. Ghasemi, M. Fardi, R.K. Ghaziani, Numerical solution of nonlinear delay differential equations of fractional order in reproducing Kernel Hilbert Space,Appl.Math.comput. 268 (2015) 815-831.
[7] H. Saeedi, M.M. Mohseni, N. Mollahasani, G.N. Chuev, A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order, Commun. Nonlinear Sci. Numer Simulat. 16(3) (2011) 1154-1163.
[8] K. Maleknejad, S. Sohrabi, Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets, Appl. Math. Comput. 186(1) (2007) 836-843.
[9] Y. Naunz, Variational iteration method and Homotopy perturbation method for fourth-order fractional integro-differential equations, Comput. Math. Appl., 61 (2011) 2230-2241.
[10] S.S. Ray, Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method, Commun. Nonlinear Sci. Numer. Simulate. 14 (2009) 129-306.
[11] L. Huang, X.F. Li, Y.L. Zhao, X.Y. Duan, Approximate solution of fractional integro-differential equations by Taylor expansion method, Comput. Math. Appl. 62(3) (2011) 1127-1134.
[12] S. Shahmorad, M.H. Ostadzad, D.Baleanu, A Tau-like numerical method for solving delay integro-differential equations, Applied numerical mathematics, 151 (2020) 322-336.
[13] Emad M. H. Mohamed, K.R. Raslan, K.A. Khalid, M.A. Abd El Salam, On general form of fractional delay integro-differential equations, Arab journal of basic and applied sciences,27(1) (2020) 313-323.
[14] Khadijo Rashid Adem and Chaudry Masood Khalique, On the exact explicit solutions of a generalized (2+1)dimensional Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation,Proceedings of the International Conference on Scientific Computing (CSC), 32 (2013).
[15] Biswajit Das and Dhritikesh Chakrabarty,Inversion of Matrix by Elementary Column Transformation: Representation of Numerical Data by a Polynomial Curve,International Journal of Mathematics Trends and Technology (IJMTT),42(1) (2017) 45-49.
[16] S. Sekar and K. Prabhavathi, Numerical treatment for the Nonlinear Fuzzy Differential Equations using Leapfrog Method, International Journal of Mathematics Trends and Technology (IJMTT), 26(1) (2015) 35-39.

Keywords : Fractional calculus; Chebyshev wavelets; Delay Fredholm integro-differential equations; Numerical solution.