Hadamard-Type Fractional Integro-Differential Problem: A Note on Some Asymptotic Behavior of Solutions

Autor:	Ahmad Mugbil, Nasser-Eddine Tatar
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	asymptotic behavior fractional differential equation Hadamard fractional derivative Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 6, Iss 5, p 267 (2022)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract6050267
Popis:	As a follow-up to the inherent nature of Hadamard-Type Fractional Integro-differential problem, little is known about some asymptotic behaviors of solutions. In this paper, an integro-differential problem involving Hadamard fractional derivatives is investigated. The leading derivative is of an order between one and two whereas the nonlinearities may contain fractional derivatives of an order between zero and one as well as some non-local terms. Under some reasonable conditions, we prove that solutions are asymptotic to logarithmic functions. Our approach is based on a generalized version of Bihari–LaSalle inequality, which we prove. In addition, several manipulations and crucial estimates have been used. An example supporting our findings is provided.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/7a22cbaac41543b1b59a875d0cdadb0b Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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