scholarly journals A note for the Ulam-Hyers-Rassias stability of differential equations on bounded intervals

2021 ◽  
Vol 9 (3) ◽  
pp. 35-41
Author(s):  
Serkan Aslıyüce ◽  
Süleyman Öğrekçi
Keyword(s):  
Differential Equations ◽  
Rassias Stability

scholarly journals Stability of Unbounded Differential Equations in Menger k-Normed Spaces: A Fixed Point Technique

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 400 ◽  
Author(s):  
Masoumeh Madadi ◽  
Reza Saadati ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Normed Spaces ◽  
Fixed Point Technique ◽  
Rassias Stability

We attempt to solve differential equations υ ′ ( ν ) = Γ ( ν , υ ( ν ) ) and use the fixed point technique to prove its Hyers–Ulam–Rassias stability in Menger k-normed spaces.

scholarly journals On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Dongming Nie ◽  
Azmat Ullah Khan Niazi ◽  
Bilal Ahmed
Keyword(s):  
Differential Equations ◽  
Existence Of A Solution ◽  
Neutral Differential Equations ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Functional Differential ◽  
Schauder Theorem ◽  
Equations With Delay ◽  
Rassias Stability ◽  
Fractional Functional

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.

scholarly journals On existence and stability results for nonlinear fractional delay differential equations

2018 ◽  
Vol 36 (4) ◽  
pp. 55-75 ◽  
Author(s):  
Kishor D. Kucche ◽  
Sagar T. Sutar
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Existence And Stability ◽  
Fractional Delay ◽  
Delay Differential ◽  
Rassias Stability

We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hyers--Rassias stability, $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability and generalized $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability of fractional order delay differential equations.

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 Ulam-Hyers stability of Darboux-Ionescu problem

2021 ◽  
Vol 37 (2) ◽  
pp. 211-216
Author(s):  
DANIELA MARIAN ◽  
SORINA ANAMARIA CIPLEA ◽  
NICOLAE LUNGU
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Darboux Problem ◽  
Partial Differential ◽  
Doctoral Thesis ◽  
Rassias Stability

In his doctoral thesis, D. V. Ionescu has considered Darboux problem for partial differential equations of order two with modified argument. The Darboux-Ionescu problem was studied in some general cases by I. A. Rus. In this paper we study Ulam-Hyers stability and Ulam-Hyers-Rassias stability for this problem considered by I. A. Rus, using inequalities of Wendorff type.

scholarly journals k-Generalized Ψ-Hilfer differential equations in Banach spaces

2021 ◽  
Author(s):  
Salim Abdelkrim ◽  
Mouffak Benchohra ◽  
Jamal Lazreg ◽  
Gaston NGuerekata
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
The Subject ◽  
Fractional Differential ◽  
Stability Results ◽  
Rassias Stability

In this paper, we prove some existence and Ulam-Hyers-Rassias stability results for a class of initial value problem for implicit nonlinear fractional differential equations and generalized Ψ-Hilfer fractional derivative in Banach spaces. The results are based on fixed point theorems of Darbo and Monch associated with the technique of measure of noncompactness. Illustrative examples are the subject of the last section.

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