Existence, uniqueness and asymptotic behavior of solutions for a fractional problem with combined nonlinearities

Fatemah Mofarreh; Adnane Hamiaz; Bilel Khamessi

doi:10.1216/rmj-2021-51-1387

Abstract

We discuss the existence and the uniqueness of solution of the fractional differential equation in $\left( {0,1} \right)$ satisfying the boundary conditions on $0$ and $1$ . Using the Schauder fixed point theorem, we give the asymptotic behavior of such solution.

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Fatemah Mofarreh. Adnane Hamiaz. Bilel Khamessi. "Existence, uniqueness and asymptotic behavior of solutions for a fractional problem with combined nonlinearities." Rocky Mountain J. Math. 51 (4) 1387 - 1398, August 2021. https://doi.org/10.1216/rmj.2021.51.1387

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Received: 8 September 2020; Revised: 5 December 2020; Accepted: 24 December 2020; Published: August 2021

First available in Project Euclid: 5 August 2021

MathSciNet: MR4298854

zbMATH: 1477.31040

Digital Object Identifier: 10.1216/rmj.2021.51.1387

Subjects:

Primary: 31C15 , 34B27 , 35K10

Keywords: fractional differential equation , Karamata regular variation theory , positive solution , Schauder fixed point theorem

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