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Mathematics 2019, 7(3), 223; https://doi.org/10.3390/math7030223

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

1
Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
2
KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
*
Author to whom correspondence should be addressed.
Received: 1 February 2019 / Revised: 16 February 2019 / Accepted: 17 February 2019 / Published: 27 February 2019
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Abstract

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. View Full-Text
Keywords: arbitrary order differential equations; multiple positive solution; Perov-type fixed point theorem; HU stability arbitrary order differential equations; multiple positive solution; Perov-type fixed point theorem; HU stability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Shah, K.; Kumam, P.; Ullah, I. On Ulam Stability and Multiplicity Results to a Nonlinear Coupled System with Integral Boundary Conditions. Mathematics 2019, 7, 223.

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