Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets

• Autorzy: Khajehnasiri Amir Ahmad , Ezzati R. , Kermani M.

Identyfikatory

DOI

10.1515/jaa-2021-2050

• Języki publikacji: EN

Abstrakty

EN

The main aim of this paper is to use the operational matrices of fractional integration of Haar wavelets to find the numerical solution for a nonlinear system of two-dimensional fractional partial Volterra integral equations. To do this, first we present the operational matrices of fractional integration of Haar wavelets. Then we apply these matrices to solve systems of two-dimensional fractional partial Volterra integral equations (2DFPVIE). Also, we present the error analysis and convergence as well. At the end, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

Słowa kluczowe

EN

two-dimensional fractional integral equation; operational matrix; error analysis; Haar wavelet; block-pulse function

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 2
• Strony: 239--257
• Opis fizyczny: Bibliogr. 34 poz., wykr.

Twórcy

autor

Khajehnasiri Amir Ahmad

• Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

autor

Ezzati R.

• Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

autor

Kermani M.

• Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran

Bibliografia

• [1] S. Abbas and M. Benchohra, Fractional order integral equations of two independent variables, Appl. Math. Comput. 227 (2014), 755-761.
• [2] E. Adams and H. Spreuer, Uniquesness and stability for boundary value problems with weakly coupled systems of nonlinear integro-differential equations and application to chemical reactions, J. Math. Anal. Appl. 49 (1975), 393-410.
• [3] N. Aghazadeh and A. A. Khajehnasiri, Solving nonlinear two-dimensional Volterra integro-differential equations by block-pulse functions, Math. Sci. (Springer) 7 (2013), Article ID 3.
• [4] S. Arbabi, A. Nazari and M. T. Darvishi, A two-dimensional Haar wavelets method for solving systems of PDEs, Appl. Math. Comput. 292 (2017), 33-46.
• [5] A. Arikoglu and I. Ozkol, Solution of fractional integro-differential equations by using fractional differential transform method, Chaos Solitons Fractals 40 (2009), no. 2, 521-529.
• [6] M. Asgari and R. Ezzati, Using operational matrix of two-dimensional Bernstein polynomials for solving two-dimensional integral equations of fractional order, Appl. Math. Comput. 307 (2017), 290-298.
• [7] J. Biazar, M. Eslami and M. R. Islam, Differential transform method for special systems of integral equations, J. King Saud Univ. Sci. 24 (2012), 211-214.
• [8] A. Ebadian, H. R. Fazli and A. A. Khajehnasiri, Solution of nonlinear fractional diffusion-wave equation by traingular functions, Se⃗MA J. 72 (2015), 37-46.
• [9] A. Ebadian and A. A. Khajehnasiri, Block-pulse functions and their applications to solving systems of higher-order nonlinear Volterra integro-differential equations, Electron. J. Differential Equations 2014 (2014), Paper No. 54.
• [10] L. Gaul, P. Klein and S. Kempfle, Damping description involving fractional operators, Mech. Syst. Signal Process 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, Hybrid Bernstein block-pulse functions for solving system of fractional integro-differential equations, Int. J. Comput. Math. 95 (2018), no. 11, 2287-2307.
• [13] M. H. Heydari, M. R. Hooshmandasl, F. Mohammadi and C. Cattani, Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations, Commun. Nonlinear Sci. Numer. Simul. 19 (2014), no. 1,37-48.
• [14] C. Hwang and Y. P. Shih, Parameter identification via Laguerre polynomials, Internat. J. Systems Sci. 13 (1982), no. 2, 209-217.
• [15] M. A. Jaswon and G. T. Symm, Integral Equation Methods in Potential Theory and Elastostatics. Computational Mathematics and Applications, Academic Press, London, 1977.
• [16] A. A. Khajehnasiri, Numerical solution of nonlinear 2D Volterra-Fredholm integro-differential equations by two-dimensional triangular function, Int. J. Appl. Comput. Math. 2 (2016), no. 4, 575-591.
• [17] A. A. Khajehnasiri, M. Afshar Kermani and R. Ezzati, Chaos in a fractional-order financial system, Int. J. Math. Oper. Res. 17 (2020), no. 3, 318-332.
• [18] A. Kilicman and Z. A. A. Al Zhour, Kronecker operational matrices for fractional calculus and some applications, Appl. Math. Comput. 187 (2007), no. 1, 250-265.
• [19] Y. Li and W. Zhao, Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Comput. 216 (2010), no. 8, 2276-2285.
• [20] H. Liu, J. Huang, W. Zhang and Y. Ma, Meshfree approach for solving multi-dimensional systems of Fredholm integral equations via barycentric Lagrange interpolation, Appl. Math. Comput. 346 (2019), 295-304.
• [21] M. Mojahedfar and A. Tari Marzabad, Solving two-dimensional fractional integro-differential equations by Legendre wavelets, Bull. Iranian Math. Soc. 43 (2017), no. 7, 2419-2435.
• [22] 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.
• [23] P. N. Paraskevopoulos, Legendre series approach to identification and analysis of linear systems, IEEE Trans. Automat. Control 30 (1985), no. 6, 585-589.
• [24] H. Rahmani Fazli, F. Hassani, A. Ebadian and A. A. Khajehnasiri, National economies in state-space of fractional-order financial system, Afr. Mat. 27 (2016), no. 3-4, 529-540.
• [25] E. A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006), no. 1, 1-6.
• [26] H. Saeedi and M. M. Moghadam, Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 3, 1216-1226.
• [27] H. Saeedi, N. Mollahasani, M. Mohseni Moghadam and G. N. Chuev, An operational Haar wavelet method for solving fractional Volterra integral equations, Int. J. Appl. Math. Comput. Sci. 21 (2011), no. 3, 535-547.
• [28] P. Schiavone, C. Constanda and A. Mioduchowski, Integral Methods in Science and Engineering, Birkhäuser, Boston, 2002.
• [29] L. Wang, Y. Ma and Z. Meng, Haar wavelet method for solving fractional partial differential equations numerically, Appl. Math. Comput. 227 (2014), 66-76.
• [30] J. Xie, Q. Huang and F. Zhao, Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations in two-dimensional spaces based on block pulse functions, J. Comput. Appl. Math. 317 (2017), 565-572.
• [31] J. Xie and M. Yi, Numerical research of nonlinear system of fractional Volterra-Fredholm integral-differential equations via block-pulse functions and error analysis, J. Comput. Appl. Math. 345 (2019), 159-167.
• [32] M. Yi and J. Huang, Wavelet operational matrix method for solving fractional differential equations with variable coefficients, Appl. Math. Comput. 230 (2014), 383-394.
• [33] M. Yi, J. Huang and J. Wei, Block pulse operational matrix method for solving fractional partial differential equation, Appl. Math. Comput. 221 (2013), 121-131.
• [34] M. Zurigat, S. Momani and A. Alawneh, Homotopy analysis method for systems of fractional integro-differential equations, Neural Parallel Sci. Comput. 17 (2009), no. 2, 169-186.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)