On the Generalized Liouville-Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions

被引：5

作者：

Awadalla, Muath ^{[1
]}

Subramanian, Muthaiah ^{[2
]}

Abuasbeh, Kinda ^{[1
]}

Manigandan, Murugesan ^{[3
]}

机构：

[1] King Faisal Univ, Coll Sci, Dept Math & Stat, Hafuf 31982, Al Ahsa, Saudi Arabia

[2] KPR Inst Engn & Technol, Dept Math, Coimbatore 641407, Tamil Nadu, India

[3] Sri Ramakrishna Mission Vidyalaya Coll Arts & Sci, Dept Math, Coimbatore 641020, Tamil Nadu, India

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 11期

关键词：

generalized fractional derivatives; generalized fractional integrals; coupled system; existence; fixed point; RIEMANN-LIOUVILLE; EXISTENCE; SYSTEM; DERIVATIVES;

D O I：

10.3390/sym14112273

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this study, we examine the existence and Hyers-Ulam stability of a coupled system of generalized Liouville-Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray-Schauder alternative and Krasnoselskii's fixed point theorem are used to demonstrate the existence of a solution. The Banach fixed point theorem's concept of contraction mapping is used in the second theorem to emphasise the analysis of uniqueness, and the results for Hyers-Ulam stability are established in the next theorem. We establish the stability of Ulam-Hyers using conventional functional analysis. Finally, examples are used to support the results. When a generalized Liouville-Caputo (rho) parameter is modified, asymmetric results are obtained. This study presents novel results that significantly contribute to the literature on this topic.

引用

页数：22

共 27 条

[1] Existence and uniqueness results for a nonlinear coupled system involving Caputo fractional derivatives with a new kind of coupled boundary conditions [J].