Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality

Shahram Rezapour, Sotiris K. Ntouyas, Abdelkader Amara, Sina Etemad and Jessada Tariboon
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Shahram Rezapour: Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Abdelkader Amara: Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
Jessada Tariboon: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Mathematics, 2021, vol. 9, issue 11, 1-22

Abstract: The main intention of the present research study is focused on the analysis of a Caputo fractional integro-differential boundary problem (CFBVP) in which the right-hand side of supposed differential equation is represented as a sum of two nonlinear terms. Under the integro-derivative boundary conditions, we extract an equivalent integral equation and then define new operators based on it. With the help of three distinct fixed-point theorems attributed to Krasnosel’ski?, Leray–Schauder, and Banach, we investigate desired uniqueness and existence results. Additionally, the dependence criterion of solutions for this CFBVP is checked via the generalized version of the Gronwall inequality. Next, three simulative examples are designed to examine our findings based on the procedures applied in the theorems.

Keywords: caputo derivative; fixed point; integral equation; generalized Gronwall inequality (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 (1)

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