×
Alizadeh, Reza; Jahangiri Rad, M.; Ebadian, Ali; Dastmalchi, F.

Reproducing kernel method for solving partial two-dimensional nonlinear fractional Volterra integral equation. (English) Zbl 07708016

J. Mahani Math. Res. Cent. 12, No. 2, 325-337 (2023).
Summary: This article discusses the replicating kernel interpolation collocation method related to Jacobi polynomials to solve a class of fractional system of equations. The reproducing kernel function that is executed as an (RKM) was first created in the form of Jacobi polynomials. To prevent Schmidt orthogonalization, researchers compare the numerical solutions achieved by varying the parameter value. Through various numerical examples, it is demonstrated that this technique is practical and precise.

MSC:

65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

reproducing; shifted Jacobi polynomials; two-dimensional fractional integral equation; fractional derivatives
Cite Review PDF
Full Text: DOI

References:

[1] [1] M. H. Heydari, M.R. Hooshmandasl, F.M. Maalek Ghaini, C. Cattani. A computational method for solving stochastic Ito-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, Journal of Computational Physics, 270 (2014) 402-415. · Zbl 1349.65711
[2] [2] E. Babolian, M. Mordad. A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions, Computers and Mathematics with Applications, 62 (2011) 187-198. · Zbl 1228.65243
[3] [3] M. H. Heydari, M.R. Hooshmandasl, F. M. Maalek Ghaini, C. Cattani. An ecient computational method for solving nonlinear stochastic Ito integral equations: Application for stochastic problems in physics, Journal of Computational Physics, 283 (2015) 148-168. · Zbl 1351.60088
[4] [4] F. Mirzaee, E. Hadadiyan. Application of two-dimensional hat functions for solving space-time integral equations, J. Appl. Math. Comput, 4 (2015) 1-34. · Zbl 1328.65276
[5] [5] M. Safavi, A.A. Khajehnasiri. Numerical solution of nonlinear mixed Volterra-Fredholm integro-di erential equations by two-dimensional block-pulse functions, Cogent Mathematics and Statistics, 5 (2018) 1-12. · Zbl 1426.65219
[6] [6] M.P. Tripathi, V. K. Baranwal, R. K. Pandey, O. P. Singh. A new numerical algorithm to solve fractional di erential equations based on operational matrix of generalized hat functions, Commun Nonlinear Sci Numer Simulat, 18 (2013) 1327-1340. · Zbl 1284.65086
[7] [7] H. Rahmani Fazli, F. Hassani, A. Ebadian, A. A. Khajehnasiri. National economies in state-space of fractional-order nancial system, Afrika Matematika, 10 (2015) 1-12. · Zbl 1405.91438
[8] [8] M. Saeedi, M.M. Moghadam. Numerical solution of nonlinear Volterra integrodi erential equations of arbitrary order by CAS Wavelets, Commun Nonlinear Sci Numer Simulat, 16 (2011) 1216-1226. · Zbl 1221.65140
[9] [9] C. Shekher Singh, H. Singh Vineet, K. Singh, O. P. Singh Fractional order operational matrix methods for fractional singular integro-di erential equation, Applied Mathematical Modelling, 40 (2016) 10705-10718. · Zbl 1443.65446
[10] [10] S. Momani, M. A. Noor. Numerical methods for fourth-order fractional integrodi erential equations, Appl. Math. Comput, 182 (2006) 754-760. · Zbl 1107.65120
[11] [11] M. Safavi, A. A. Khajehnasiri. Numerical solution of nonlinear mixed Volterra-Fredholm integro-di erential equations by two-dimensional block-pulse functions, Cogent Mathematics & Statistics, 1 (2018) 152-184 . · Zbl 1426.65219
[12] [12] M. Safavi, A. A. Khajehnasiri, A. Jafari, J. Banar. A New Approach to Numerical Solution of Nonlinear Partial Mixed Volterra-Fredholm Integral Equations via Two-Dimensional Triangular Functions, Malaysian Journal of Mathematical Sciences, 3 (2021) 489{507.} · Zbl 1483.65229
[13] [13] M. Abbaszadeh, M. Dehghan, A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped di usion-wave equation, Applied Numerical Mathematics, 169 (2021) 44-63. · Zbl 1486.65157
[14] [14] H. Saeedi, G. N. Chuev Triangular functions for operational matrix of nonlinear fractional Volterra integral equations, Journal of Applied Mathematics and Computing, 49 (2015) 213-232. · Zbl 1329.65323
[15] [15] M. M. Moghadam, H.Saeedi, N. Razaghzadeh, A spectral Chelyshkov wavelet method to solve systems of nonlinear weakly singular Volterra integral equations, Journal of mahani mathematical research center, 9 (2020) 1-20. · Zbl 1488.65754
[16] [16] S. Ahmad, A. Ahmad, K. Ali, H. Bashir, M. F. Iqbal. E ect of non-Newtonian ow due to thermally-dependent properties over an inclined surface in the presence of chemical reaction, Brownian motion and thermophoresis, Alexandria Engineering Journal, 221 (2021) 4931-4945.
[17] [17] A. A. Khajehnasiri. Numerical Solution of Nonlinear 2D Volterra-Fredholm Integro-Di erential Equations by Two-Dimensional Triangular Function, Int. J. Appl. Comput.Math 2, (2016) 575-591. · Zbl 1420.65138
[18] [18] X. Li, H. Li, B. Wu, Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments Applied Mathematics and Computation, 349 (2019) 304-313. · Zbl 1429.65135
[19] [19] S. G. Esfahani, S. S. Foroushani, M. Azhari, On the use of reproducing kernel particle nite strip method in the static, stability and free vibration analysis of FG plates with di erent boundary conditions and diverse internal supports, Applied Mathematical Modelling, 92 (2021), 380-409 · Zbl 1481.74250
[20] [20] A.A. Khajehnasiri, M. Safavi, Solving fractional Black{Scholes equation by using Boubaker functions, Mathematical Methods in the Applied Sciences, 11 (2022) 8505-8515.} · Zbl 1486.91092
[21] [21] M. Safavi, A.A. Khajehnasiri, Solutions of the Rakib-Sivashinsky Equation With Time-and Space-Fractional Derivatives, Southeast Asian Bulletin of Mathematics, 5 (2015) 695{704.} · Zbl 1349.35405
[22] [22] S. Chena S. Soradi Zeid, H. Dutta, M. Mesrizadehd, Y. Chu, Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay Chaos, Solitons and Fractals, 144 (2021) 755-761. · Zbl 1498.34063
[23] [23] T. Allahviranloo, H. Sahihi, Reproducing kernel method to solve fractional delay di erential equations, Applied Mathematics and Computation, 400 (2021) 2419-2435. · Zbl 1508.34079
[24] [24] N. Boudi, Z. Ennadi , Change of representation and the rigged Hilbert space formalism in quantum mechanics, Reports on Mathematical Physics, 87 (2021) 145-166. · Zbl 07371587
[25] [25] F. Mirzaee, E. Hadadiyan. Numerical solution of linear Fredholm integral equations via two-dimensional modi cation of hat functions, Applied Mathematics and Computation 250 (2015) 805-816. · Zbl 1328.65276
[26] [26] ] I. Podlubny. Fractional Di erential Equations, Academic Press, San Diego, 1999. · Zbl 0924.34008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.