A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay

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dc.authoridAli, Md. Shajib/0000-0002-3992-8821
dc.contributor.authorLiaqat, Muhammad Imran
dc.contributor.authorKhan, Adnan
dc.contributor.authorAkgul, Ali
dc.contributor.authorAli, Md. Shajib
dc.date.accessioned2024-12-24T19:29:49Z
dc.date.available2024-12-24T19:29:49Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractSome researchers have combined two powerful techniques to establish a new method for solving fractional-order differential equations. In this study, we used a new combined technique, known as the Elzaki residual power series method (ERPSM), to offer approximate and exact solutions for fractional multipantograph systems (FMPS) and pantograph differential equations (PDEs). In Caputo logic, the fractional-order derivative operator is measured. The Elzaki transform method and the residual power series method (RPSM) are combined in this novel technique. The suggested technique is based on a new version of Taylor's series that generates a convergent series as a solution. Establishing the coefficients for a series, like the RPSM, necessitates computing the fractional derivatives each time. As ERPSM just requires the concept of a zero limit, we simply need a few computations to get the coefficients. The novel technique solves nonlinear problems without the need for He's and Adomian polynomials, which is an advantage over the other combined methods based on homotopy perturbation and Adomian decomposition methods. The relative, recurrence, and absolute errors of the problems are analyzed to evaluate the efficiency and consistency of the presented method. Graphical significances are also identified for various values of fractional-order derivatives. As a result, the procedure is quick, precise, and easy to implement, and it yields outstanding results.
dc.identifier.doi10.1155/2022/6333084
dc.identifier.issn2314-8896
dc.identifier.issn2314-8888
dc.identifier.scopus2-s2.0-85134671802
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1155/2022/6333084
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7251
dc.identifier.volume2022
dc.identifier.wosWOS:000829493500001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherHindawi Ltd
dc.relation.ispartofJournal of Function Spaces
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.titleA Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay
dc.typeArticle

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