On the Existence and Uniqueness of Solutions of Fractional Dynamic Equations On Time Scales

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2022

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Yokohama Publ

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

The existence and uniqueness of solutions of Cauchy problem for a nonlinear Caputo fractional dynamic equation of arbitrary order alpha > 0 is studied. The problem is treated as a fixed point problem posed on a b-metric space. A numerical example is presented to support the theoretical results.

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Erhan, Inci M./0000-0001-6042-3695
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Erhan, Inci M. ORCID logo

Keywords

Time scale, Caputo fractional dynamic equation, fixed point, b-metric

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Volume

23

Issue

8

Start Page

1545

End Page

1558

URI

https://hdl.handle.net/20.500.14411/8991

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