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 Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
A. Javadian ◽  
E. Sorouri ◽  
G. H. Kim ◽  
M. Eshaghi Gordji
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Open Interval ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form , with condition that there exists a nonzero in such that and is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.

scholarly journals Hyers-Ulam stability of exact second-order linear differential equations

2012 ◽  
Vol 2012 (1) ◽  
pp. 36 ◽  
Author(s):  
Mohammed Bagher Ghaemi ◽  
Madjid Eshaghi Gordji ◽  
Badrkhan Alizadeh ◽  
Choonkil Park
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
Linear Differential

scholarly journals Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Yongjin Li ◽  
Yan Shen
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Linear Differential ◽  
The Stability

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second ordery′′+p(x)y′+q(x)y+r(x)=0. That is, iffis an approximate solution of the equationy′′+p(x)y′+q(x)y+r(x)=0, then there exists an exact solution of the equation near tof.

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