scholarly journals On the Hyers-Ulam Stability of Differential Equations of Second Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Qusuay H. Alqifiary ◽  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Second Order ◽  
Gronwall Inequality ◽  
Ulam Stability ◽  
Grönwall Inequality

By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.

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 Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 230
Author(s):  
Juan-Carlos Cortés ◽  
Ana Navarro-Quiles ◽  
José-Vicente Romero ◽  
María-Dolores Roselló
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Random Variable ◽  
Second Order ◽  
Singular Points ◽  
Linear Differential Equations ◽  
Transformation Technique ◽  
Order Linear ◽  
Bessel Differential Equation ◽  
Linear Differential

In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.

scholarly journals Oscillation in deviating differential equations using an iterative method

2019 ◽  
Vol 27 (2) ◽  
pp. 143-169 ◽  
Author(s):  
George E. Chatzarakis ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Gronwall Inequality ◽  
Deviating Arguments ◽  
First Order ◽  
Grönwall Inequality ◽  
Nonnegative Coefficients ◽  
First Order Differential Equations

AbstractSufficient oscillation conditions involving lim sup and lim inf for first-order differential equations with non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Grönwall inequality. Examples, numerically solved in MATLAB, are also given to illustrate the applicability and strength of the obtained conditions over known ones.

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 On the generalized superstability of nth-order linear differential equations with initial conditions

2015 ◽  
Vol 98 (112) ◽  
pp. 243-249 ◽  
Author(s):  
Jinghao Huang ◽  
Qusuay Alqifiary ◽  
Yongjin Li
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Constant Coefficients ◽  
Linear Differential

We establish the generalized superstability of differential equations of nth-order with initial conditions and investigate the generalized superstability of differential equations of second order in the form of y??(x) + p(x)y?(x)+q(x)y(x) = 0 and the superstability of linear differential equations with constant coefficients with initial conditions.

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