Three-variable eighth-kind Chebyshev polynomials for two-dimensional multiterm time-fractional diffusion–wave equations

Khadijeh Sadri; David Amilo; Evren Hinçal; Mahmoud A. Zaky; Khadijeh Sadri; David Amilo; Evren Hinçal; Mahmoud A. Zaky

doi:10.3934/math.20261192

AIMS Mathematics

2026, Volume 11, Issue 9: 30091-30124. doi: 10.3934/math.20261192

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Research article

Three-variable eighth-kind Chebyshev polynomials for two-dimensional multiterm time-fractional diffusion–wave equations

1.
Mathematics Research Center, Near East University, Mersin 10, Nicosia 99138, Turkey
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

Received: 04 April 2026 Revised: 15 June 2026 Accepted: 29 June 2026 Published: 16 September 2026
MSC : 35C11, 35Q79, 41A10, 65M70

Three-variable eighth-kind Chebyshev polynomials are employed as basis functions to construct a pseudo-operational collocation method. The proposed approach is applied to solve two-dimensional multiterm time-fractional diffusion–wave equations (three variables corresponding to two spatial variables and one temporal variable). The existence and uniqueness of the solution to the considered problem are established using Krasnoselskii's fixed-point theorem. An upper bound for the residual function is derived in a suitable weighted space, showing that the use of a finite number of basis functions provides an accurate approximate solution. Several illustrative examples are presented to demonstrate the applicability, accuracy, and computational efficiency of the proposed scheme for high-dimensional partial differential equations.
Citation: Khadijeh Sadri, David Amilo, Evren Hinçal, Mahmoud A. Zaky. Three-variable eighth-kind Chebyshev polynomials for two-dimensional multiterm time-fractional diffusion–wave equations[J]. AIMS Mathematics, 2026, 11(9): 30091-30124. doi: 10.3934/math.20261192

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Abstract

Three-variable eighth-kind Chebyshev polynomials are employed as basis functions to construct a pseudo-operational collocation method. The proposed approach is applied to solve two-dimensional multiterm time-fractional diffusion–wave equations (three variables corresponding to two spatial variables and one temporal variable). The existence and uniqueness of the solution to the considered problem are established using Krasnoselskii's fixed-point theorem. An upper bound for the residual function is derived in a suitable weighted space, showing that the use of a finite number of basis functions provides an accurate approximate solution. Several illustrative examples are presented to demonstrate the applicability, accuracy, and computational efficiency of the proposed scheme for high-dimensional partial differential equations.

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