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Designing a matrix collocation method for fractional delay integro-differential equations with weakly singular kernels based on vieta–fibonacci polynomials

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dc.contributor.author Sadri, Khadijeh
dc.contributor.author Hosseini, Kamyar
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Salahshour, Soheil
dc.contributor.author Park, Choonkil
dc.date.accessioned 2024-03-05T12:59:34Z
dc.date.available 2024-03-05T12:59:34Z
dc.date.issued 2022-01
dc.identifier.citation Sadri, Khadijeh;...et.al. (2022). "Designing a matrix collocation method for fractional delay integro-differential equations with weakly singular kernels based on vieta–fibonacci polynomials", Fractal and Fractional, Vol.6, No.1. tr_TR
dc.identifier.issn 25043110
dc.identifier.uri http://hdl.handle.net/20.500.12416/7468
dc.description.abstract In the present work, the numerical solution of fractional delay integro-differential equations (FDIDEs) with weakly singular kernels is addressed by designing a Vieta–Fibonacci collocation method. These equations play immense roles in scientific fields, such as astrophysics, economy, control, biology, and electro-dynamics. The emerged fractional derivative is in the Caputo sense. By resultant operational matrices related to the Vieta–Fibonacci polynomials (VFPs) for the first time accompanied by the collocation method, the problem taken into consideration is converted into a system of algebraic equations, the solving of which leads to an approximate solution to the main problem. The existence and uniqueness of the solution of this category of fractional delay singular integro-differential equations (FDSIDEs) are investigated and proved using Krasnoselskii’s fixed-point theorem. A new formula for extracting the VFPs and their derivatives is given, and the orthogonality of the derivatives of VFPs is easily proved via it. An error bound of the residual function is estimated in a Vieta–Fibonacci-weighted Sobolev space, which shows that by properly choosing the number of terms of the series solution, the approximation error tends to zero. Ultimately, the designed algorithm is examined on four FDIDEs, whose results display the simple implementation and accuracy of the proposed scheme, compared to ones obtained from previous methods. Furthermore, the orthogonality of the VFPs leads to having sparse operational matrices, which makes the execution of the presented method easy. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.3390/fractalfract6010002 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Caputo Derivative Operator tr_TR
dc.subject Error Bound tr_TR
dc.subject Fractional Delay Integro-Differential Equation With Weakly Singular Kernel tr_TR
dc.subject Vieta–Fibonacci Polynomials tr_TR
dc.title Designing a matrix collocation method for fractional delay integro-differential equations with weakly singular kernels based on vieta–fibonacci polynomials tr_TR
dc.type article tr_TR
dc.relation.journal Fractal and Fractional tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 6 tr_TR
dc.identifier.issue 1 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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