Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces

By Jinrong Wang, Akbar Zada, Wajid Ali. International journal of nonlinear sciences and numerical simulation, 2018

53 citations recorded by the source corpus.

Abstract In this paper, Ulam’s-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman–Grönwall–Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of α$\alpha$-Ho¨$\ddot{o}$lder’s condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi–Banach spaces which is best suited for obtaining results under the assumptions of α$\alpha$-Ho¨$\ddot{o}$lder’s condition.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b57022858d70a8238da6572e4df63b332510fa73

Citations in the corpus

• Stability analysis of a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem (2019, unknown): “(39) Put (39) in (38) and taking maximum of both side, we get ‖‖p(u) − p(ū)‖‖ ≤ [ 3Tp2Γ(p + 1) + Γ(2 − r)Tp2Γ(p − r + 1) ] ⎡⎢⎢⎣ 11 −2 −4 T𝜎𝜎Γ(𝛿) + 3T𝜎 𝜎Γ(𝛿)(1 −2 −4 T𝜎 𝜎Γ(𝛿) ) ⎤⎥⎥⎦ ||𝑦 − ?”