Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings

Mohammed K. A. Kaabar, Ahmed Refice, Mohammed Said Souid, Francisco Martínez, Sina Etemad, Zailan Siri and Shahram Rezapour
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Mohammed K. A. Kaabar: Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
Ahmed Refice: Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, Sidi bel Abbes 22000, Algeria
Mohammed Said Souid: Department of Economic Sciences, University of Tiaret, Tiaret 14035, Algeria
Francisco Martínez: Department of Applied Mathematics and Statistics, Technological University of Cartagena, 30203 Cartagena, Spain
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
Zailan Siri: Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran

Mathematics, 2021, vol. 9, issue 14, 1-17

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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