An operational matrix approach with Vieta-Fibonacci polynomial for solving generalized Caputo fractal-fractional differential equations

This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo-type differential equations with fractal-fractional terms. Based on the proposed approach, the fractal-fractional differential equations with...

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Bibliographic Details
Published inAin Shams Engineering Journal Vol. 15; no. 5; p. 102678
Main Authors S M, Sivalingam, Kumar, Pushpendra, Govindaraj, V., Qahiti, Raed Ali, Hamali, Waleed, Mutum, Zico Meetei
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2024
Elsevier
Subjects
Convergence
Error bound
Fractal-fractional derivatives
Operational matrix
Vieta-Fibonacci polynomials
Operational matrix
Error bound
Vieta-Fibonacci polynomials
Fractal-fractional derivatives
Convergence
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Summary:This study developed and examined a new operational matrix approach utilizing the Vieta-Fibonacci polynomial for the numerical solution of generalized Caputo-type differential equations with fractal-fractional terms. Based on the proposed approach, the fractal-fractional differential equations with generalized Caputo-type derivatives were reduced into a system of algebraic equations, which was further solved to obtain the unknown solution. The convergence and error bounds are theoretically calculated. The results are quantitatively confirmed in various cases. To demonstrate the correctness and computational efficacy of this proposed technique, it is compared to other well-known methods.
ISSN:2090-4479
DOI:10.1016/j.asej.2024.102678