A New Method to Solve Dual Systems of Fractional Integro-Differential Equations by Legendre Wavelets
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Authors: R. KAVEHSARCHOGHA, R. EZZATI, N. KARAMIKABIR AND F. M. YAGHOBBI
DOI: 10.46793/KgJMat2106.951K
Abstract:
The method that will be presented, is numerical solution based on the Legendre wavelets for solving dual systems of fractional integro-differential equations (FIDEs). First of all we make the operational matrix of fractional order integration. The application of this matrix is transforming FIDEs to a system of algebric equations. By this changing, we are able to solve it by a simple solution. In this way, the Legendre wavelets and their operator matrix are the most important keys of our solution. After explaining the method we test on some illustrative examples which numerical solutions of these examples demonstrate the validity and applicability of suggested method.
Keywords:
Legendre wavelets, fractional integro-differential equations, algebraic, dual systems.
References:
[1] A. Avudainayagam and C. Vant, Wavelet-Galerkin method for integro-differential equations, Appl. Numer. Math. 32(3) (2000), 247–254.
[2] E. Babolian and F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operetional matrix of integration, Appl. Math. Comput. 188(1) (2007), 417–426.
[3] C. K. Chur, Wavelets: A Mathematical Tool for Signal Analysis, Siam, Philadelphia, 1997.
[4] K. Goyal and M. Mehra, An adaptive meshfree spectral gragh wavelet method for partial differential equations, Appl. Numer. Math. 113 (2017), 168–185.
[5] M. H. Heydari, M. R. Hooshmanddasl and F. Mohammadib, Legendre wavelet method for solving fractional patial differential equations with Dirichlet boundary conditions, Appl. Math. Comput. 234 (2014), 267–276.
[6] M. H. Heydari, M. R. Hooshmanddasl, F. M. Maalekahaini and F. Mohummdi, Wavelet collocation method for solving multi order fractional differential equations, J. Appl. Math. (2012), Article ID 542401, 19 pages.
[7] M. H. Heydari, M. R. Hooshmanddasl, C. Cattani and M. Li, Legendre wavelets method for solving fractional population growth model in a closed system, Math. Probl. Eng. (2013), Article ID 161030, 8 pages.
[8] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
[9] C. H. Hsiao and S. P. Wu, Numerical solution of time-varying functional differential equations via Haar wavelets, Appl. Math. Comput. 188(1) (2007), 1049–1058.
[10] H. Jafari, S. A. Yousefi, M. A. Firoozjaee, S. Momani and C. M. Khalique, Application of Legendre wavelets for solving fractional differential equations, J. Comput. Appl. Math. 62 (2011), 1038–1045.
[11] E. Keshavarz, Y. Ordokhani and M. Razzaghi, Bernoulli wavelet operetional matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Model. 38(24) (2014), 6038–6051.
[12] E. Keshavarz, Y. Ordokhania and M. Razzaghib, The Taylor wavelet method for solving the initial and boundary value problems of Bratu-type equations, Appl. Numer. Math. 128 (2018), 205–216.
[13] V. V. Kulish and J. L. Lage, Application of fractional calculus to fluid mechanics, Journal of Fluids Engineering 3 (2002), 803–806.
[14] S. Lal and V. K. Sharma, On wavelet approximation of a function by Legendre wavelet methods, Funct. Anal. Approx. Comput. 9(2) (2017), 11–19.
[15] Y. Li and K. Shah, Numerical solution of coupled systems of fractional order partial differential equations, Adv. Math. Phys. (2017), 14 pages.
[16] Y. Li and N. Sun, Numerical solution of fractional differential equations using the generalized block puls operational matrix, J. Comput. Appl. Math. 62 (2011), 1046–1054.
[17] F. Mohamad and C. Cattani, A generelized fractional order Legendre wavelet Tau method for solving fractional differential equations, J. Comput. Appl. Math. 339 (2017), 306–316.
[18] S. Momani and R. Qaralleh, An efficient method for solving systems of fractional integro-differential equations, Comput. Math. Appl. 52 (2006), 459–470.
[19] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, USA 1999.
[20] M. Razzaghi and S. Yousefi, Legendre wavelets operational matrix of integration, Internat. J. Systems Sci. 32 (2001), 495–502.
[21] J. Wang, T. Z. Xu, Y. Q. Wei and J. Q. Xie, Numerical simulation for coupled systems of nonlinear order integro-differential equations via wavelets method, Appl. Math. Comput 324 (2018), 36–50.
[22] M. X. Yi, L. F. Wang and J. Huang, Legendre wavelet method for the numerical solution of fractional integro-differential equations with weakly singular kernel, Appl. Math. Model. 40 (2016), 3422–3437.
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