On The Solutions of Fractional Boundary Value Problems for a Combined Caputo Fractional Differential Equations

Authors

  • Şuayip Toprakseven Artvin Vocational School, Accounting and Taxation, Artvin Çoruh University, Artvin, 08100, Turkey https://orcid.org/0000-0003-3901-9641

DOI:

https://doi.org/10.37256/cm.4220232314

Keywords:

positive solutions, fractional differential equation, combined Caputo derivative, fractional Maxwell model

Abstract

In this paper, a new class of fractional boundary value problem with the combined Caputo derivative is proposed and the physical interpretation of this new derivative has been explained. Under some assumptions, the positive solutions of the fractional differential equation with the help of Leray-Schauder and Krasnoselskii's fixed point theorems in a cone have been investigated. Moreover, the solution of the fractional Maxwell models involving the combined Caputo derivative by using the extended Laplace transform is obtained. Finally, some examples are given to support theoretical findings.

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Published

2023-04-01

How to Cite

1.
Toprakseven Şuayip. On The Solutions of Fractional Boundary Value Problems for a Combined Caputo Fractional Differential Equations. Contemp. Math. [Internet]. 2023 Apr. 1 [cited 2024 Mar. 4];4(2):202-16. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2314