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2019•MathematicsOpen access

Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Akbar Zada, Shaheen Fatima, Zeeshan Ali, Jiafa Xu, Yujun Cui

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Abstract

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

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What this paper is about

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

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Available abstract

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

Key concepts: Uniqueness, Mathematics, Fixed-point theorem, Contraction principle, Contraction mapping, Picard–Lindelöf theorem, Nonlinear system, Schauder fixed point theorem

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