Solving fractional two-dimensional nonlinear weakly singular partial integro-differential equation by using Fibonacci polynomials

[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] E. Adams and H. Spreuer, Uniqueness and stability for boundary value problems with weakly coupled of nonlinear integro-differential equations and application to chemical reactions, J. Math. Anal. Appl. 49 (1975), 393–410.

[3] E. Babolian, K. Maleknejad, M. Roodaki and H. Almasieh, Two-dimensional triangular functions and their applications to nonlinear 2D Volterra–Fredholm integral equations, Comput. Math. Appl.60 (2010), 1711–1722.

[4] O. Baghani, Second Chebyshev wavelets (SCWs) method for solving finite-time fractional linear quadratic optimal control problems, Math. Comput. Simul. 17 (2020), 31–47.

[5] S. Davaeifar and J. Rashidinia, Boubaker polynomials collocation approach for solving systems of nonlinear Volterra–Fredholm integral equations, J. Taibah Unive. Sci. 6 (2017), 1182–1199.

[6] K.D. Dwivedi and J. Singh, Numerical solution of two-dimensional fractional-order reaction advection subdiffusion equation with finite-difference Fibonacci collocation method, Math. Comput. Simul. 270 (2021), 38–50.

[7] 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. Diff. Equ. 54 (2014), 1–9.

[8] M. Irfan and F.A. Shah, Fibonacci wavelet method for solving the time-fractional bioheat transfer model, Optik 95 (2021), 644–651.

[9] M. Irfan, F.A. Shah and K.S. Nisar, Fibonacci wavelet method for solving Pennes bioheat transfer equation, Int. J. Wavelets Multiresol. Inf. Process. 95 (2020), 644–651.

[10] C. Hwang and Y.P. Shih, Parameter identification via Laguerre polynomials, Internat, J. Syst. Sci. 13 (1982), 209–217.

[11] A.A. Khajehnasiri and R. Ezzati, Boubaker polynomials and their applications for solving fractional two-dimensional nonlinear partial integro-differential Volterra integral equations, Comput. Appl. Math. 41 (2022),

46–56.

[12] A.A. Khajehnasiri, R. Ezzati and M. Afshar Kermani, Solving fractional two-dimensional nonlinear partial Volterra integral equation by using Bernoulli wavelet, Ira. J. Sci. Technol. Trans. A: Sci. 72 (2021), 983–995.

[13] A.A. Khajehnasiri, R. Ezzati and M. Afshar Kermani, Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets, J. Appl. Anal. 27 (2021), 1–21.

[14] A.A. Khajehnasiri, R. Ezzati and A. Jafari Shaerlar, Walsh functions and their applications to solving nonlinear fractional Volterra integro-differential equation, Int. J. Nonlinear Anal. Appl. 12 (2021), 1577–1589.

[15] V.L. Khatskevich, Some properties of Legendre polynomials and an approximate solution of the Black–Scholes equation governing option pricing, Differ. Equa. 53 (2015), 1157—1164.

[16] E. Keshavarz, Y. Ordokhani and M. Razzaghi, The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations, Appl. Math. Comput. 351 (2019), 83–98.

[17] K. Maleknejad, H. Almasieh and M. Roodaki, Triangular functions (TF) method for the solution of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput. 149 (2004), 799–806.

[18] F. Mirzaee, S. Alipour and N. Samadyar, A numerical approach for solving weakly singular partial integro differential equations via two-dimensional-orthonormal Bernstein polynomials with the convergence analysis, Numer. Meth. Partial Differ. Equ. 102 (2018), 1–24.

[19] F. Mirzaee and S.F. Hoseini, A Fibonacci collocation method for solving a class of Fredholme-Volterra integral equations in two-dimensional spaces, Beni-Suef Univer. J. Basic Appl. Sci. 270 (2014), 157–163.

[20] S. Mojahedfar and A. Tari Marzabad, Solving two-dimensional fractional integro-diffrential equations by Legendre wavelets, Bull. Iran. Math. Soc. 43 (2017), 2419–2435.

[21] S. Nematia, P.M. Limab and Y. Ordokhani, Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials, J. Comput. Appl. Math. 242 (2013), 53–69.

[22] V.K. Patel, S. Singh, V.K. Singh and E. Tohidi, Two Dimensional wavelets collocation Scheme for linear and nonlinear volterra weakly singular partial integro-differential equations, Int. J. Appl. Comput. Math. 132 (2018), 1–27.

[23] K. Rabiei and Y. Ordokhani, Solving fractional pantograph delay differential equations via fractional-order Boubaker polynomials, Engin. Comput. 2 (2017), 1013—1026.

[24] K. Rabiei and Y. Ordokhani, Boubaker Hybrid Functions and their Application to Solve Fractional Optimal Control and Fractional Variational Problems, Appl. Math. 5 (2018), 541–567.

[25] K. Rabiei, Y. Ordokhani and E. Babolian, Fractional-order Boubaker functions and their applications in solving delay fractional optimal control problems, J. Vibration Control 15 (2017), 1–14.

[26] 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), 529–540.

[27] E.A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006), 1–6.

[28] S. Rezabeyk, S. Abbasbandy and E. Shivanian, Solving fractional-order delay integro-differential equations using operational matrix based on fractional-order Euler polynomials, Math. Sci. 14 (2020), 97–107.

[29] W. Rudin, Principles of Mathematical Analysis, 3rd ed. New York, 1976.

[30] S. Sabermahani and Y. Ordokhani, Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis, J. Vibration Control 19 (2020), 1–15.

[31] S. Sabermahani, Y. Ordokhani and S.A. Yousefi, Fibonacci wavelets and their applications for solving two classes of time-varying delay problems, Optim. Control Appl. Meth. 17 (2019), 1–22.

[32] S. Sabermahani, Y. Ordokhani and S.A. Yousefi, Numerical scheme for solving singular fractional partial integrodifferential equation via orthonormal Bernoulli polynomials, Int. J. Numer. Mode. 351 (2019), 73–88.

[33] N. Samadyar and F. Mirzaee, Numerical scheme for solving singular fractional partial integro-differential equation via orthonormal Bernoulli polynomials, Int. J. Numer. Mode. 351 (2019), 73–88.

[34] P. Schiavone, C. Constanda and A. Mioduchowski, Integral Methods in Science and Engineering, Birkhauser, Boston, 2002.

[35] F.A. Shah, M. Irfan, K.S. Nisar, R.T. Matoog and E.E. Mahmoud, Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions, Results Phys. 24 (2021), 104–123.

[36] S.C. Shiralashetti and L. Lamani, Fibonacci wavelet based numerical method for the solution of nonlinear Stratonovich Volterra integral equations, Sci. Afr. 176 (2020), 1–11.

[37] Y. Talaei and M. Asgari, An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations, Neural Comput. Appl. 343 (2018), 1369-–1376.

[38] J. Wang, T. Xu, Y. Wei and J. Xie, Numerical simulation for coupled systems of nonlinear fractional order integro-differential equations via wavelets method, Applied Math. Comput. 324 (2018), 36–50.

[39] M. Yi and J. Huang, Wavelet operational matrix method for solving fractional differential equations with variable coefficients, Appl. Math. Comput. 230 (2014), 383–394.

[40] 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.

[41] I. Zamanpour and R. Ezzati, Operational matrix method for solving fractional weakly singular 2D partial Volterra integral equations, J. Comput. Appl. Math. 419 (2023), 1–19.