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Full-Text Articles in Physical Sciences and Mathematics
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
Turkish Journal of Mathematics
In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor …
Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana
Principal Parts Of A Vector Bundle On Projective Line And The Fractional Derivative, Hafiz Syed Husain, Mariam Sultana
Turkish Journal of Mathematics
This work is an exposition on computational aspects of principal parts of a vector bundle on projective line over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizing infinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for the possibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study follows theapproachproposedbyVasilyTarasov. The difference is that Tarasov proposeda geometric interpretation using finite order jet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf of real projective line as its formal algebraic …