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Walsh functions and their applications to solving nonlinear fractional Volterra integro-differential equation | ||
International Journal of Nonlinear Analysis and Applications | ||
دوره 12، شماره 2، بهمن 2021، صفحه 1577-1589 اصل مقاله (506.86 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.19846.2108 | ||
نویسندگان | ||
Amirahmad Khajehnasiri1؛ Reza Ezzati* 2؛ Akbar Jafari Shaerlar3 | ||
1Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran | ||
2Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran | ||
3Department of Mathematics, Khalkhal Branch, Islamic Azad University, Khalkhal, Iran | ||
تاریخ دریافت: 28 بهمن 1398، تاریخ بازنگری: 26 اردیبهشت 1400، تاریخ پذیرش: 07 تیر 1400 | ||
چکیده | ||
In this article, we extended an efficient computational method based on Walsh operational matrix to find an approximate solution of nonlinear fractional order Volterra integro-differential equation, First, we present the fractional Walsh operational matrix of integration and differentiation. Then by applying this method, the nonlinear fractional Volterra integro-differential equation is reduced into a system of algebraic equation. The benefits of this method are the low-cost of setting up the equations without applying any projection method such as collocation, Galerkin, etc. The results show that the method is very accuracy and efficiency. | ||
کلیدواژهها | ||
Walsh functions؛ Operational matrix. Block-pulse functions؛ Fractional calculus | ||
مراجع | ||
[1] N. Aghazadeh and A.A. Khajehnasiri, Solving nonlinear two-dimensional Volterra integro-differential equations by block-pulse functions, Math. Sci. , 7 (2013) 1–6. [2] M. Asgari and R. Ezzati, Using operational matrix of two-dimensional Bernstein polynomials for solving twodimensional integral equations of fractional order, Appl. Math. Comput. 307 (2017) 290-298. [3] E. Babolian and M. Mordad, A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions, Comput. Math. Appl. 62 (2011) 187–198. [4] V. Balachandran and K. Murugesan, Analysis of electronic circuits using the single-term Walsh series approach, Int. J. Elect. 69 (1990) 327–322. [5] V. Balakumar and K. Murugesan, Single-Term Walsh series method for systems of linear volterra integral equations of the second kind, Appl. Math. Comput. 228 (2014) 371–376. [6] R. Chandra Guru Sekar and K. Murugesan, Numerical solutions of nonlinear system of higher order volterra integro-differential equations using generalized STWS technique, Diff. Equ. Dyn. Syst. 60 (2017) 1-13. [7] R. Chandra Guru Sekar and K. Murugesan, Single term walsh series method for the system of nonlinear delay volterra integro-differential equations describing biological species living together, Int. J. Appl. Comput. Math. 42 (2018) 1–13. [8] C. F. Chen and Y. T. Tsay, Walsh operational matrices for fractional calculus and their application to distributed systemes, J. Franklin Inst. 303 (1977) 267–284. [9] A. Ebadian and A. A. Khajehnasiri, Block-pulse functions and their applications to solving systems of higher-order nonlinear Volterra integro-differential equations, Elect. J. Diff. Equ. (2014) 1–9. [10] L. Gaul, P. Klein and S. Kempfle, Damping description involving fractional operators, Mech. Syst. Signal Proc. 5 (1991) 81–88. [11] W.G. Glockle and T.F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J. 68 (1995) 46–53.[12] E. Hesameddini and M. Shahbazi, Two-dimensional shifted Legendre polynomials operational matrix method for solving the two-dimensional integral equations of fractional order, Appl. Math. Comput. 322 (2018) 40–54. [13] A. A. Khajehnasiri, R. Ezzati and M. Afshar Kermani. Chaos in a fractional-order financial system, Int. J. Math. Oper. Res. 17 (2020) 318–332. [14] A. A. Khajehnasiri, R. Ezzati and M. Afshar Kermani, Solving fractional two-dimensional nonlinear partial Volterra integral equation by using bernoulli wavelet, Iran. J. Sci. Tech. Trans. Sci. (2021) 1–13. [15] A. A. Khajehnasiri and M. Safavi, Solving fractional Black-Scholes equation by using Boubaker functions, Math. Meth. Appl. Sci. 39 (2021) 1–11. [16] S. Mashayekbi and M. Razzaghi, Numerical solution of nonlinear fractional integro-differential equation by hybrid functions, Engin. Anal. Boundary Elem. 56 (2015) 81–89. [17] S. Momani and M. Aslam Noor, Numerical methods for fourth-order fractional integro-differential equations, Appl. Math. Comput. 182 (2006) 754–760. [18] S. Najafalizadeh and R. Ezzati, Numerical methods for solving two-dimensional nonlinear integral equations of fractional order by using two-dimensional block pulse operational matrix, Appl. Math. Comput. 280 (2016) 46–56. [19] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [20] P. Rahimkhani and Y. Ordokhani, Approximate solution of nonlinear fractional integro-differential equations using fractional alternative Legendre functions, J. Appl. Math. Comput. 311 (2020) 1–19. [21] H. Rahmani Fazli, F. Hassani, A. Ebadian and A.A. Khajehnasiri, National economies in state-space of fractionalorder financial system, Afrika Mat. 10 (2015) 1-12. [22] H. Rahmani Fazli, F. Hassani, A. Ebadian and A.A. Khajehnasiri, National economies in state-space of fractionalorder financial system, Afrika Mat. 27 (2016) 529-540. [23] G.P. Rao, K.R. Palanisamy and T. Srinirasan, Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems, Trans. Autom. Cont. 25 (1980) 317–319. [24] N. Rohaninasab, K.Maleknjad and R. Ezzati, Numerical solution of high-order volterra-fredholm integrodifferential equation by using Legendre collocation method, Appl. Math. Comput. 328 (2018) 171–188. [25] S. Sahafay, On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation, Appl. Math. Comput. 218 (2012) 5239–5248. | ||
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