scholarly journals β–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 231 ◽  
Author(s):  
Xiaoming Wang ◽  
Muhammad Arif ◽  
Akbar Zada
Keyword(s):  
Differential Equations ◽  
Type Inequality ◽  
Impulsive System ◽  
Evolution Family ◽  
Compact Interval ◽  
Ulam Stability ◽  
Basic Tool ◽  
Unbounded Interval ◽  
Nonautonomous Differential Equations ◽  
Rassias Stability

In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the β –Ulam stability, β –Hyers–Ulam stability and β –Hyers–Ulam–Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.

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 A Generalized ML-Hyers-Ulam Stability of Quadratic Fractional Integral Equation

2021 ◽  
Vol 10 (1) ◽  
pp. 414-427
Author(s):  
Mohammed K. A. Kaabar ◽  
Vida Kalvandi ◽  
Nasrin Eghbali ◽  
Mohammad Esmael Samei ◽  
Zailan Siri ◽  
...  
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Differential Equations ◽  
Fractional Integral ◽  
Future Research ◽  
Ulam Stability ◽  
Science And Engineering ◽  
Fractional Integral Equation ◽  
Rassias Stability

Abstract An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The generalized ML–Hyers–Ulam stability is established in this investigation. We study both of the Hyers–Ulam stability (HUS) and ML–Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed differential equation (DEq). Our proposed technique unifies various differential equations’ classes. Therefore, this technique can be further applied in future research works with applications to science and engineering.

scholarly journals Aboodh transform and the stability of second order linear differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramdoss Murali ◽  
Arumugam Ponmana Selvan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
Linear Differential ◽  
The Stability ◽  
Rassias Stability

AbstractIn this paper, we introduce a new integral transform, namely Aboodh transform, and we apply the transform to investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability, Mittag-Leffler–Hyers–Ulam stability, and Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

scholarly journals Existence and Stability of Implicit Fractional Differential Equations with Stieltjes Boundary Conditions Involving Hadamard Derivatives

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-36
Author(s):  
Danfeng Luo ◽  
Mehboob Alam ◽  
Akbar Zada ◽  
Usman Riaz ◽  
Zhiguo Luo
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Ulam Stability ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Cone Type ◽  
Fractional Differential ◽  
Rassias Stability ◽  
Implicit Fractional Differential Equations

In this article, we make analysis of the implicit fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We use some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer’s fixed point theorem, and Leray–Schauder result of the cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability by using the classical technique of functional analysis. At the end, the results are verified with the help of examples.

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

2018 ◽  
Vol 19 (7-8) ◽  
pp. 763-774 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Ulam Stability ◽  
Point Boundary ◽  
New Class ◽  
Fractional Differential ◽  
The Given ◽  
Rassias Stability ◽  
Sequential Fractional Differential Equations

AbstractThis 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.

scholarly journals Ulam-Hyers-Rassias stability of pseudoparabolic partial differential equations

2015 ◽  
Vol 31 (2) ◽  
pp. 233-240
Author(s):  
NICOLAIE LUNGU ◽  
◽  
SORINA ANAMARIA CIPLEA ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ulam Stability ◽  
Partial Differential ◽  
New Applications ◽  
Rassias Stability

The aim of this paper is to give some types of Ulam stability for a pseudoparabolic partial differential equation. In this case we consider Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. We investigate some new applications of the Gronwall lemmas to the Ulam stability of a nonlinear pseudoparabolic partial differential equations.

scholarly journals Ulam stability for delay fractional differential equations with a generalized Caputo derivative

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5265-5274 ◽  
Author(s):  
Raad Ameen ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Ulam Stability ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Equations With Delay ◽  
Rassias Stability

The objective of this paper is to extend Ulam-Hyers stability and Ulam-Hyers-Rassias stability theory to differential equations with delay and in the frame of a certain class of a generalized Caputo fractional derivative with dependence on a kernel function. We discuss the conditions such delay generalized Caputo fractional differential equations should satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To demonstrate our results two examples are presented.

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