Existence and U-H-R stability of solutions to the implicit nonlinear fbvp in the variable order settings

Authors

• Mohammed K. A. Kaabar
• Ahmed Refice
• Mohammed Said Souid
• Francisco Martinez
• Sina Etemad
• Zailan SiriFollow
• Shahram Rezapour

Document Type

Article

Publication Date

7-1-2021

Abstract

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii's fixed point theorem and in the sequel, and its Ulam-Hyers-Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.

Keywords

Variable-order operators, Piecewise constant functions, Ulam-Hyers-Rassias stability, Implicit problem, Fixed point theorems

Publication Title

Mathematics

Recommended Citation

Kaabar, Mohammed K. A.; Refice, Ahmed; Souid, Mohammed Said; Martinez, Francisco; Etemad, Sina; Siri, Zailan; and Rezapour, Shahram, "Existence and U-H-R stability of solutions to the implicit nonlinear fbvp in the variable order settings" (2021). Research Publications (2021 to 2025). 12526.
https://knova.um.edu.my/research_publications_2021_2025/12526

Divisions

MathematicalSciences

Volume

9

Issue

14

Publisher

MDPI

Publisher Location

ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND