On Existence and Asymptotic Behavior of Positive Solutions for a Fractional Order Differential System Involving Riemann–Liouville Derivatives

Sameh Turki

doi:10.1007/s12591-023-00634-1

On Existence and Asymptotic Behavior of Positive Solutions for a Fractional Order Differential System Involving Riemann–Liouville Derivatives

Sameh Turki^*

^*Corresponding author for this work

Department of Basic Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we investigate the existence and the asymptotic behavior of positive solutions of a boundary value problem defined by a system of coupled fractional differential equations involving Riemann–Liouville derivatives. The existence result is given by means of fixed point theory and the asymptotic behavior of such a solution is derived with the aid of Karamata regular variation theory.

Original language	English
Pages (from-to)	419-452
Number of pages	34
Journal	Differential Equations and Dynamical Systems
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s12591-023-00634-1
State	Published - Apr 2025

Keywords

Asymptotic behavior
Green function
Karamata function
Riemann–Liouville fractional derivative
Schäuder’s fixed point theorem

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10.1007/s12591-023-00634-1

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title = "On Existence and Asymptotic Behavior of Positive Solutions for a Fractional Order Differential System Involving Riemann–Liouville Derivatives",

abstract = "In this article, we investigate the existence and the asymptotic behavior of positive solutions of a boundary value problem defined by a system of coupled fractional differential equations involving Riemann–Liouville derivatives. The existence result is given by means of fixed point theory and the asymptotic behavior of such a solution is derived with the aid of Karamata regular variation theory.",

keywords = "Asymptotic behavior, Green function, Karamata function, Riemann–Liouville fractional derivative, Sch{\"a}uder{\textquoteright}s fixed point theorem",

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PY - 2025/4

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N2 - In this article, we investigate the existence and the asymptotic behavior of positive solutions of a boundary value problem defined by a system of coupled fractional differential equations involving Riemann–Liouville derivatives. The existence result is given by means of fixed point theory and the asymptotic behavior of such a solution is derived with the aid of Karamata regular variation theory.

AB - In this article, we investigate the existence and the asymptotic behavior of positive solutions of a boundary value problem defined by a system of coupled fractional differential equations involving Riemann–Liouville derivatives. The existence result is given by means of fixed point theory and the asymptotic behavior of such a solution is derived with the aid of Karamata regular variation theory.

KW - Asymptotic behavior

KW - Green function

KW - Karamata function

KW - Riemann–Liouville fractional derivative

KW - Schäuder’s fixed point theorem

UR - https://www.scopus.com/pages/publications/105003397727

U2 - 10.1007/s12591-023-00634-1

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M3 - Article

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SN - 0971-3514

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JO - Differential Equations and Dynamical Systems

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ER -

On Existence and Asymptotic Behavior of Positive Solutions for a Fractional Order Differential System Involving Riemann–Liouville Derivatives

Abstract

Keywords

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