Stability Analysis of Multi-point Boundary Value Problem for Sequential Fractional Differential Equations with Non-instantaneous Impulses

By Akbar Zada, Sartaj Ali. International journal of nonlinear sciences and numerical simulation, 2018

66 citations recorded by the source corpus.

Abstract This paper deals with a new class of non-linear impulsive sequential fractional differential equations with multi-point boundary conditions using Caputo fractional derivative, where impulses are non instantaneous. We develop some sufficient conditions for existence, uniqueness and different types of Ulam stability, namely Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability and generalized Hyers–Ulam–Rassias stability for the given problem. The required conditions are obtained using fixed point approach. The validity of our main results is shown with the aid of few examples.

View Paper: https://www.semanticscholar.org/paper/835a13d6d4e697fdfd6d63356c458445022473a1

Citations in the corpus

• Stability analysis of a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem (2019, unknown): “By using (49) and (50), we have ||u − v|| ≤ ( 3Tp 2Γ(p + 1) + Γ(2 − r)Tp 2Γ(p − r + 1) ) ε + ( 3Tp 2Γ(p + 1) + Γ(2 − r)T p 2Γ(p − r + 1) )”