Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials

M. Usman, M. Hamid, T. Zubair, R.U. Haq, Weining Wang and M.B. Liu

Applied Mathematics and Computation, 2020, vol. 372, issue C

Abstract: Accurate solutions of nonlinear multi-dimensional delay problems of fractional-order arising in mathematical physics and engineering recently have been found to be a challenging task for the research community. This paper witnesses that an efficient fully spectral operational matrices-based scheme is developed and successfully applied for stable solutions of time-fractional delay differential equations (DDEs). Monomials are introduced in order to proposed the novel operational matrices for fractional-order integration Iν and derivative Dν by means of shifted Gegenbauer polynomials. Some ordinary and partial delay differential equations of fractional-order are considered to show reliability, efficiency and appropriateness of the proposed method. In order to approximate the delay term in DDEs a novel delay operational matrix Θba is introduced with the help of shifted Gegenbauer polynomials. The proposed algorithm transform the problem understudy into a system of algebraic equations which are easier to tackle. Analytical solutions of the mentioned problem are effectively obtained, and an inclusive comparative study is reported which reveals that the proposed computational scheme is effective, accurate and well-matched to investigate the solutions of aforementioned problems. Error bound analysis is enclosed in our investigation to reveal the consistency and support the mathematical formulation of the algorithm. This proposed scheme can be extended to explore the solution of more dervisfy problem of physical nature in complex geometry.

Keywords: Shifted Gegenbauer polynomials; Delay differential equation; Operational matrix; Fractional calculus (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309774

DOI: 10.1016/j.amc.2019.124985

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