On Ulam Stability and Multiplicity Results to a Nonlinear Coupled System with Integral Boundary Conditions

被引：2
|
作者：
Shah, Kamal [1 ]
Kumam, Poom [2 ]
Ullah, Inam [1 ]
机构：
[1] Univ Malakand, Dept Math, Chakdara Dir L 18800, Khyber Pakhtunk, Pakistan
[2] KMUTT, KMUTT Fixed Point Res Lab, KMUTT Fixed Point Theory & Applicat Res Grp, Theoret & Computat Sci Ctr TaCS,Fac Sci, Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok 10140, Thailand
来源：
MATHEMATICS | 2019年 / 7卷 / 03期
关键词：
arbitrary order differential equations; multiple positive solution; Perov-type fixed point theorem; HU stability; DIFFERENTIAL-EQUATIONS; POSITIVE SOLUTIONS; FRACTIONAL ORDER; EXISTENCE; UNIQUENESS;
D O I：
10.3390/math7030223
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This manuscript is devoted to establishing existence theory of solutions to a nonlinear coupled system of fractional order differential equations (FODEs) under integral boundary conditions (IBCs). For uniqueness and existence we use the Perov-type fixed point theorem. Further, to investigate multiplicity results of the concerned problem, we utilize Krasnoselskii's fixed-point theorems of cone type and its various forms. Stability analysis is an important aspect of existence theory as well as required during numerical simulations and optimization of FODEs. Therefore by using techniques of functional analysis, we establish conditions for Hyers-Ulam (HU) stability results for the solution of the proposed problem. The whole analysis is justified by providing suitable examples to illustrate our established results.
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页数：20
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