The Existence of Solution to Fractional Boundary Value Problem with Riemann-Liouville Type History-State-Based Variable-Order Derivative

Authors

  • Shuqin Zhang Department of Mathematics, China University of Mining and Technology Beijing, Beijing, China
  • Jie Wang College of Mathematics and Statistics, Shangqiu Normal University, Shangqiu, China

DOI:

https://doi.org/10.37256/cm.3420221652

Keywords:

fractional differential equations, Riemann-Liouville type variable-order derivative, boundary value problem, existence of solution, Hölder space

Abstract

The paper is devoted to studying the solutions of boundary value problem for nonlinear fractional differential equation with Riemann-Liouville type history-state-based variable-order derivative. Using Schauder fixed point theorem and Banach fixed point thoerem, we prove the existence and uniqueness of solutions in the Hölder space. Lastly, two examples are given to show the applicability of the existence theorems.

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Published

2022-11-19

How to Cite

1.
Zhang S, Wang J. The Existence of Solution to Fractional Boundary Value Problem with Riemann-Liouville Type History-State-Based Variable-Order Derivative. Contemporary Mathematics [Internet]. 2022 Nov. 19 [cited 2022 Dec. 1];3(4):525-51. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1652