Qualitative Behaviour of a Caputo Fractional Differential System

In this article, we investigate a new system of fractional differential equations with integral boundary conditions. The proposed problem contains Caputo fractional derivative operators, integer derivatives and Riemann integral boundary values. We get the existence and uniqueness of solutions for th...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2023-12, Vol.22 (4), Article 143
Main Authors: Fan, Ruixiong, Yan, Nan, Yang, Chen, Zhai, Chengbo
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Derivatives
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Fixed points (mathematics)
Fractional calculus
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:In this article, we investigate a new system of fractional differential equations with integral boundary conditions. The proposed problem contains Caputo fractional derivative operators, integer derivatives and Riemann integral boundary values. We get the existence and uniqueness of solutions for the new system of fractional differential equations based on a fixed point theorem of increasing ϕ -( h ,  e )-concave operators. The results show that the unique solution exists in a given set and can be approximated by making an iterative sequence for any initial point in the given set. Further, an example is given to illustrate the effectiveness and applicability of our main results.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-023-00836-6