Abstract
In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to obtain conditions for the existence and uniqueness of positive solutions. We discuss Hyers–Ulam (HU) type stability of the concerned solutions and provide an example for illustration of the obtained results.
Highlights
The fractional calculus is one of the most emerging areas of investigation
Our work is concerned with implicit-type coupled systems of fractional differential equations (FODEs) with impulsive conditions
Coupled systems of FODEs have been studied extensively in the last few decades because in applied sciences, we deal with many physical problems that can be modeled via these systems
Summary
The fractional calculus is one of the most emerging areas of investigation. The fractional differential operators are used to model many physical phenomena in a much better form as compared to ordinary differential operators, which are local. Definition 3 ([48]) The coupled system (1) is said to be HU stable if there exists Kα,β = max{Kα, Kβ } > 0 such that, for = max{ α, β } > 0 and for every solution (ξ , μ) ∈ B of the inequality. Definition 5 ([48]) The coupled system (1) is said to be HU-Rassias stable with respect to Φα,β if there exists a constant KΦα,Φβ such that, for some > 0 and for any approximate solution (ξ , μ) ∈ B of the inequalities. Definition 6 ([48]) The coupled system (1) is said to be GHU-Rassias stable with respect to Φα,β if there exists a constant KΦα,Φβ such that, for any approximate solution (ξ , μ) ∈ B of inequality (5), there exists a unique solution (θ, σ ) ∈ B of (1) satisfying (ξ , μ)(t) – (θ, σ )(t) ≤ KΦα,Φβ Φα,β (t), t ∈ J. The considered coupled system (1) has at least one solution
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