Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (5) ◽  
pp. 1231-1248
Author(s):  
Danfeng Luo ◽  
Zhiguo Luo
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence Results ◽  
Time Varying ◽  
Ulam Stability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Gronwall’S Inequality ◽  
Fractional Differential ◽  
Delay Differential ◽  
Stability Results

AbstractIn this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing generalized Grönwall’s inequality. Some results in this literature are new and improve some early conclusions.

scholarly journals Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Manzoor Ahmad ◽  
Jiafa Xu ◽  
...  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Coupled Systems ◽  
Ulam Stability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Uniqueness Results ◽  
Fractional Differential

This work is committed to establishing the assumptions essential for at least one and unique solution of a switched coupled system of impulsive fractional differential equations having derivative of Hadamard type. Using Krasnoselskii’s fixed point theorem, the existence, as well as uniqueness results, is obtained. Along with this, different kinds of Hyers–Ulam stability are discussed. For supporting the theory, example is provided.

scholarly journals A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 647 ◽  
Author(s):  
Kui Liu ◽  
Michal Fečkan ◽  
JinRong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Compact Interval ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Stability Results ◽  
Rassias Stability

In this paper, we study Hyers–Ulam and Hyers–Ulam–Rassias stability of nonlinear Caputo–Fabrizio fractional differential equations on a noncompact interval. We extend the corresponding uniqueness and stability results on a compact interval. Two examples are given to illustrate our main results.

scholarly journals Further results on Ulam stability for a system of first-order nonsingular delay differential equations

2020 ◽  
Vol 53 (1) ◽  
pp. 225-235
Author(s):  
Akbar Zada ◽  
Bakhtawar Pervaiz ◽  
Jehad Alzabut ◽  
Syed Omar Shah
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Graphical Representation ◽  
Ulam Stability ◽  
First Order ◽  
Delay Differential ◽  
Unbounded Intervals ◽  
Ulam Type Stability

AbstractThis paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

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