×

Construction of operational matrices based on linear cardinal B-spline functions for solving fractional stochastic integro-differential equation. (English) Zbl 1490.65310


MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45R05 Random integral equations
65C30 Numerical solutions to stochastic differential and integral equations
60H20 Stochastic integral equations
65D07 Numerical computation using splines
Full Text: DOI

References:

[1] Asgari, M., Block pulse approximation of fractional Stochastic integro-differential equation, Commun. Numer. Anal., 2014, 1-7 (2014) · doi:10.5899/2014/cna-00212
[2] Alipour, S.; Mirzaee, F., An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: a combined successive approximations method with bilinear spline interpolation, Appl. Math. Comput., 371, 124947 (2020) · Zbl 1433.65344
[3] Atanackovic, TM; Stankovic, B., On a system of differential equations with fractional derivatives arising in rod theory, J. Phys. A-Math. Gen., 37, 4, 1241-1250 (2004) · Zbl 1059.35011 · doi:10.1088/0305-4470/37/4/012
[4] De Boor, CA, Practical Guide to Spline (1978), New York: Springer, New York · Zbl 0406.41003 · doi:10.1007/978-1-4612-6333-3
[5] Cioica, PA; Dahlke, S., Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains, Int. J. Comput. Math., 89, 18, 2443-2459 (2012) · Zbl 1411.60093 · doi:10.1080/00207160.2011.631530
[6] Dimov, I., Venelin, T.: Error Analysis of Biased stochastic algorithms for the second kind Fredholm integral equation. In: Innovative Approaches and Solutions in Advanced Intelligent Systems, pp. 3-16. Springer, Berlin (2016)
[7] Diop, M.; Caraballo, T., Asymptotic stability of neutral stochastic functional integro-dierential equations with impulses, Electron. Commun. Probab., 20, 1 (2015) · Zbl 1308.93212 · doi:10.1214/ECP.v19-3036
[8] Evans, RM; Katugampola, UN; Edwards, DA, Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem, Comput. Math. Appl., 73, 1346 (2017) · Zbl 1409.65114 · doi:10.1016/j.camwa.2016.12.005
[9] He, JH, Nonlinear oscillation with fractional derivative and its applications, Int. Conf. Vibrat. Eng., 98, 288-291 (1998)
[10] He, JH, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol., 15, 2, 86-90 (1999)
[11] Hilfer, R., Applications of fractional calculus in physics (2000), Singapore: World Scientific, Singapore · Zbl 0998.26002 · doi:10.1142/3779
[12] Ichiba, T., Karatzas, I., Prokaj, V., Yan, M.: Stochastic integral equations for Walsh semi martingales. arXiv:1505.02504 (2015) · Zbl 1391.60090
[13] Jankovic, S.; Ilic, D., One linear analytic approximation for stochastic integro-differential equations, Acta Mathematica Scientia, 308, 4, 1073-1085 (2010) · Zbl 1240.60153 · doi:10.1016/S0252-9602(10)60104-X
[14] Kilbas, AA; Srivastava, HM; Trujillo, JJ, Theory and Applications of Fractional Differential Equations (2006), San Diego: Elsevier, San Diego · Zbl 1092.45003
[15] Lakestani, M.; Dehghan, M.; Irandoust-pakchin, S., The construction of operational matrix of fractional derivatives using B-spline functions, Commun. Nonlinear Sci. Numer. Simulat., 17, 1149-1162 (2012) · Zbl 1276.65015 · doi:10.1016/j.cnsns.2011.07.018
[16] Ma, X.; Huang, Ch, Numerical solution of fractional integro-differential equations by a hybrid collocation method, Appl. Math. Comput., 219, 6750-6760 (2013) · Zbl 1290.65130
[17] Milovanovic, GV; Udovicic, Z., Calculation of coefficients of a cardinal B-spline, Appl. Math. Lett., 23, 1346-1350 (2010) · Zbl 1197.65021 · doi:10.1016/j.aml.2010.06.029
[18] Mirzaee, F.; Hamzeh, A., A computational method for solving nonlinear stochastic Volterra integral equations, J. Comput. Appl. Math., 306, 166-178 (2016) · Zbl 1416.65542 · doi:10.1016/j.cam.2016.04.012
[19] Mirzaee, F.; Alipour, S., An efficient cubic B-spline and bicubic B-spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations, Math. Methods Appl. Sci., 43, 1, 384-397 (2019) · Zbl 1452.65019 · doi:10.1002/mma.5890
[20] Mirzaee, F.; Alipour, S., Cubic B-spline approximation for linear stochastic integro-differential equation of fractional order, J. Comput. Appl. Math., 366, 112440 (2020) · Zbl 1483.65221 · doi:10.1016/j.cam.2019.112440
[21] Mirzaee, F.; Alipour, S., Quintic B-spline collocation method to solve n-dimensional stochastic Ito-Volterra integral equations, J. Comput. Appl. Math., 384, 113153 (2021) · Zbl 1462.65223 · doi:10.1016/j.cam.2020.113153
[22] Mirzaee, F.; Alipour, S.; Samadyar, N., Numerical solution based on hybrid of block-pulse and parabolic func- tions for solving a system of nonlinear stochastic It-Volterra integral equations of fractional order, J. Comput. Appl. Math., 349, 157-171 (2019) · Zbl 1405.60103 · doi:10.1016/j.cam.2018.09.040
[23] Mirzaee, F.; Samadyar, N., Application of Bernoulli wavelet method for estimating a solution of linear stochastic It-Volterra integral equations, Multidiscip. Model. Mater. Struct., 15, 3, 575-598 (2019) · doi:10.1108/MMMS-04-2018-0075
[24] Mirzaee, F.; Samadyar, N., Application of hat basis functions for solving two-dimensional stochastic fractional integral equations, Comput. Appl. Math., 37, 4, 4899-4916 (2018) · Zbl 1402.60082 · doi:10.1007/s40314-018-0608-4
[25] Mirzaee, F.; Samadyar, N., Application of orthonormal Bernstein polynomials to construct a efficient scheme for solving fractional stochastic integro-differential equation, Opt. Int. J. Light Electron. Opt., 132, 262-273 (2017) · doi:10.1016/j.ijleo.2016.12.029
[26] Mirzaee, F., Samadyar, N.: Implicit meshless method to solve 2D fractional stochastic Tricomi- type equation defined on irregular domain occurring in fractal transonic flow. Numer. Methods Part. Differ. Equ. (2020)
[27] Mirzaee, F.; Samadyar, N., Euler polynomial solutions of nonlinear stochastic It-Volterra integral equations, J. Comput. Appl. Math., 330, 574-585 (2018) · Zbl 1376.65004 · doi:10.1016/j.cam.2017.09.005
[28] Mirzaee, F.; Samadyar, N., On the numerical solution of fractional stochastic integro-differential equations via meshless discrete collocation method based on radial basis functions, Eng. Anal. Bound. Elem., 100, 246-255 (2019) · Zbl 1464.65010 · doi:10.1016/j.enganabound.2018.05.006
[29] Mirzaee, F.; Samadyar, N., On the numerical solution of stochastic quadratic integral equations via operational matrix method, Math. Methods Appl. Sci., 41, 12, 4465-4479 (2018) · Zbl 1461.65270 · doi:10.1002/mma.4907
[30] Mohammadi, F., A wavelet-based computational method for solving stochastic It \({\hat{o}} \)-Volterra integral equations, J. Comput. Phys., 298, 254-265 (2015) · Zbl 1349.65717 · doi:10.1016/j.jcp.2015.05.051
[31] Mohammadi, F., A wavelet Galerkin method for solving stochastic fractional differential equations, J. Fract. Calc. Appl., 7, 1, 73-86 (2016) · Zbl 1488.65014
[32] Nadeem, M., Dabas, J.: Existence of solution for fractional integro-differential equation with impulsive effect. In: Mathematical Analysis and its Applications, pp. 373-380. Springer India (2015) · Zbl 1337.45004
[33] Panda, R.; Dash, M., Fractional generalized splines and signal processing, Signal Process, 86, 2340-2350 (2006) · Zbl 1172.65315 · doi:10.1016/j.sigpro.2005.10.017
[34] Picchini, U., Julie, F.: Stochastic differential equation mixed effects models for tumor growth and response to treatment (2016)
[35] Saha, S.; Singh, S., Numerical solution of nonlinear stochastic It-Volterra integral equations driven by fractional Brownian motion, Math. Methods Appl. Sci., 41, 4, 1410-1423 (2020) · Zbl 1390.60253
[36] Samadyar, N.; Mirzaee, F., Orthonormal Bernoulli polynomials collocation approach for solving stochastic It-Volterra integral equations of Abel type, Int. J. Numer. Model. Electron. Networks Devices Fields, 33, 1, e2688 (2020) · doi:10.1002/jnm.2688
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.