Hyers-Ulam stability of Hermite fuzzy differential equations and fuzzy Mellin transform

2018 ◽  
Vol 35 (3) ◽  
pp. 3721-3731 ◽  
Author(s):  
Wenjuan Ren ◽  
Zhanpeng Yang ◽  
Xian Sun ◽  
Min Qi
Keyword(s):  
Differential Equations ◽  
Mellin Transform ◽  
Ulam Stability

scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

scholarly journals Functional equations in Schwartz distributions and their stabilities

2009 ◽  
Vol 3 (1) ◽  
pp. 14-26
Author(s):  
Jae-Young Chung
Keyword(s):  
Differential Equations ◽  
Functional Equations ◽  
Ulam Stability ◽  
Smooth Functions ◽  
Schwartz Distributions

Employing two methods we consider a class of n-dimensional functional equations in the space of Schwartz distributions. As the first approach, employing regularizing functions we reduce the equations in distributions to classical ones of smooth functions and find the solutions. Secondly, using differentiation in distributions, converting the functional equations to differential equations and find the solutions. Also we consider the Hyers-Ulam stability of the equations.

scholarly journals Hyers-Ulam Stability and Existence Criteria for the Solution of Second-Order Fuzzy Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Noor Jamal ◽  
Muhammad Sarwar ◽  
M. Motawi Khashan
Keyword(s):  
Differential Equations ◽  
Physical Model ◽  
Unique Solution ◽  
Second Order ◽  
Ulam Stability ◽  
Existence Criteria ◽  
Sumudu Transforms

In this paper, existence, uniqueness, and Hyers-Ulam stability for the solution of second-order fuzzy differential equations (FDEs) are studied. To deal a physical model, it is required to insure whether unique solution of the model exists. The natural transform has the speciality to converge to both Laplace and Sumudu transforms only by changing the variables. Therefore, this method plays the rule of checker on the Laplace and Sumudu transforms. We use natural transform to obtain the solution of the proposed FDEs. As applications of the established results, some nontrivial examples are provided to show the authenticity of the presented work.

scholarly journals Bounds for solutions of linear differential equations and Ulam stability

2020 ◽  
Vol 21 (2) ◽  
pp. 653
Author(s):  
Florina Blaga ◽  
Laura Mesaroş ◽  
Dorian Popa ◽  
Georgiana Pugna ◽  
Ioan Raşa
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Linear Differential

scholarly journals On Solvability Conditions for a Certain Conjugation Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 234
Author(s):  
Vladimir Vasilyev ◽  
Nikolai Eberlein
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Mellin Transform ◽  
Algebraic Equations ◽  
Conjugation Problem ◽  
Solvability Conditions ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.

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