scholarly journals Mahgoub transform and Hyers-Ulam stability of $ n^{th} $ order linear differential equations

2021 ◽  
Vol 7 (4) ◽  
pp. 4992-5014
Author(s):  
S. Deepa ◽  
◽  
S. Bowmiya ◽  
A. Ganesh ◽  
Vediyappan Govindan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Transform Method ◽  
Order Linear ◽  
Constant Coefficients ◽  
Linear Differential

<abstract><p>The main aim of this paper is to investigate various types of Hyers-Ulam stability of linear differential equations of $ n^{th} $ order with constant coefficients using the Mahgoub transform method. We also show the Hyers-Ulam constants of these differential equations and give some main results.</p></abstract>

scholarly journals Hyers–Ulam stability of first-order linear differential equations using Aboodh transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramdoss Murali ◽  
Arumugam Ponmana Selvan ◽  
Sanmugam Baskaran ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Differential Equations ◽  
Stability Constants ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Transform Method ◽  
Order Linear ◽  
First Order ◽  
Constant Coefficients ◽  
Linear Differential

AbstractThe main aim of this paper is to investigate various types of Ulam stability and Mittag-Leffler stability of linear differential equations of first order with constant coefficients using the Aboodh transform method. We also obtain the Hyers–Ulam stability constants of these differential equations using the Aboodh transform and some examples to illustrate our main results are given.

scholarly journals Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling

2018 ◽  
Vol 23 (4) ◽  
pp. 76
Author(s):  
Julia Gregori ◽  
Juan López ◽  
Marc Sanz
Keyword(s):  
Differential Equations ◽  
Homogeneous Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mean Square ◽  
Recent Contribution ◽  
Transform Method ◽  
Order Linear ◽  
Random Power Series ◽  
Linear Differential

The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ. 2018, 392, 1–29, doi:10.1186/s13662-018-1848-8). We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, the latter being a reformulation of our random Fröbenius method.

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

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