An iterative spectral strategy for fractional-order weakly singular integro-partial differential equations with time and space delays

Usman, M.1; Zubair, T.2; Imtiaz, J.3; Wan, C.4; Wu, W.5

2022

10.3934/era.2022090

ELECTRONIC RESEARCH ARCHIVE   影响因子和分区

2688-1594

This study aims at extending and implementing an iterative spectral scheme for fractional-order unsteady nonlinear integro-partial differential equations with weakly singular kernel. In this scheme, the unknown function u(x, t) is estimated by using shifted Gegenbauer polynomials vector Lambda(x, t), and Picard iterative scheme is used to handle underlying nonlinearities. Some novel operational matrices are developed for the first time in order to approximate the singular integral like, integral(x)(0)integral(y)(0) u(pa(1) + b(1),qa(2) + b(2), t) I (x(rho 1 )- p(rho 1))(y(rho 2) - q(rho)(2))(alpha 2) dqdp and integral(t)(0) u(gamma)(x, xi)/ (t(rho 3) - xi(rho 3) )(alpha 3) d xi , where rho' s > 1, 0 < alpha' s < 1 by means of shifted Gegenbauer polynomials vector. The advantage of this extended method is its ability to convert nonlinear problems into systems of linear algebraic equations. A computer program in Maple for the proposed scheme is developed for a sample problem, and we validate it to compare the results with existing results. Six new problems are also solved to illustrate the effectiveness of this extended computational method. A number of simulations are performed for different ranges of the nonlinearity n, alpha, fractional-order, rho, and convergence control M, parameters. Our results demonstrate that the extended scheme is stable, accurate, and appropriate to find solutions of complex problems with inherent nonlinearities.

spectral methods shifted gegenbauer polynomials fractional calculus weakly singular integral equations

SCI

英语

其他

Hong Kong RGC General Research Funds[12302219,12300520] ; NSF of China[11971221] ; Shenzhen Sci-Tech Fund["RCJC20200714114556020","JCYJ20200109115422828","JCYJ20190809150413261","JCYJ20170818153840322"]

Mathematics

Mathematics

WOS:000782907500001

AMER INST MATHEMATICAL SCIENCES-AIMS

Web of Science

1.Natl Univ Modern Languages, Dept Math, Islamabad 44790, Pakistan
2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
3.Bahria Univ, Dept Elect Engn, Islamabad, Pakistan
4.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China
5.Hong Kong Baptist Univ, Dept Math, Hong Kong, Peoples R China

Usman, M.,Zubair, T.,Imtiaz, J.,et al. An iterative spectral strategy for fractional-order weakly singular integro-partial differential equations with time and space delays[J]. ELECTRONIC RESEARCH ARCHIVE,2022,30(5).

Usman, M.,Zubair, T.,Imtiaz, J.,Wan, C.,&Wu, W..(2022).An iterative spectral strategy for fractional-order weakly singular integro-partial differential equations with time and space delays.ELECTRONIC RESEARCH ARCHIVE,30(5).

Usman, M.,et al."An iterative spectral strategy for fractional-order weakly singular integro-partial differential equations with time and space delays".ELECTRONIC RESEARCH ARCHIVE 30.5(2022).