Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions
Abstract
:1. Introduction
2. Preliminaries and Assumptions
- (A1)
- For , there exist , such thatSimilarly, for , there exist , such that
- (A2)
- For , there exist positive constant , such thatSimilarly, For , there exist positive constant , such that
- (A3)
- (A4)
- For all and for each there exists a positive constant , such thatSimilarly, for all and for each there exists a positive constant , such that
- (A5)
- For all and for each there exist positive constants , such thatSimilarly, for all and for each there exist positive constants , such that
- (A6)
- Let
- (i)
- (ii)
3. Existence and Uniqueness Analysis
4. Ulam’s Stability Analysis
- (R1)
- (R2)
- and
5. Application
6. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Chalishajar, D.; Kumar, A. Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions. Mathematics 2018, 6, 96. https://doi.org/10.3390/math6060096
Chalishajar D, Kumar A. Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions. Mathematics. 2018; 6(6):96. https://doi.org/10.3390/math6060096
Chicago/Turabian StyleChalishajar, Dimplekumar, and Avadhesh Kumar. 2018. "Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions" Mathematics 6, no. 6: 96. https://doi.org/10.3390/math6060096