Combined Liouville–Caputo Fractional Differential Equation

Autor:	McSylvester Ejighikeme Omaba, Hamdan Al Sulaimani, Soh Edwin Mukiawa, Cyril Dennis Enyi, Tijani Abdul-Aziz Apalara
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	well-posedness growth estimate asymptotic behaviours combined Liouville–Caputo fractional derivative numerical simulations stochastic models Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 7, Iss 5, p 366 (2023)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract7050366
Popis:	This paper studies a fractional differential equation combined with a Liouville–Caputo fractional differential operator, namely, LCDηβ,γQ(t)=λϑ(t,Q(t)),t∈[c,d],β,γ∈(0,1],η∈[0,1], where Q(c)=qc is a bounded and non-negative initial value. The function ϑ:[c,d]×R→R is Lipschitz continuous in the second variable, λ>0 is a constant and the operator LCDηβ,γ is a convex combination of the left and the right Liouville–Caputo fractional derivatives. We study the well-posedness using the fixed-point theorem, estimate the growth bounds of the solution and examine the asymptotic behaviours of the solutions. Our findings are illustrated with some analytical and numerical examples. Furthermore, we investigate the effect of noise on the growth behaviour of the solution to the combined Liouville–Caputo fractional differential equation.
Databáze:	Directory of Open Access Journals
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