Existence And Uniqueness Of Solutions For Fuzzy Mixed Type Of Delay Differential Equations

2021 ◽  
Vol 10 (1) ◽  
pp. 187-196
Author(s):  
D. Prasantha Bharathi ◽  
T. Jayakumar ◽  
T. Muthukumar ◽  
S. Vinoth
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Uniqueness Of Solutions ◽  
Delay Differential

scholarly journals Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

scholarly journals Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Bahar Ali Khan ◽  
Thabet Abdeljawad ◽  
Kamal Shah ◽  
Gohar Ali ◽  
Hasib Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Research Work ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Uniqueness Of The Solution ◽  
Delay Differential ◽  
Ulam Type Stability

AbstractIn this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given.

scholarly journals The existence and uniqueness theorems of fuzzy delay differential equations

2014 ◽  
Vol 10 (3) ◽  
Author(s):  
Nor Atirah Izzah Zulkefli ◽  
Normah Maan
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Realistic Model ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
New Directions ◽  
Delay Differential ◽  
Real World Problems

Delay differential equations (DDEs) arise many different phenomena including in physics, biology and chemistry. In many cases of the modeling of real world problems, information about the behaviour of a dynamical system is uncertain. In order to obtain a more realistic model, we have to take into account these uncertainties. Therefore, in this paper, we propose the existence and uniqueness theorems for fuzzy time-delay dynamical systems. We finally present some conclusions and new directions for further research in this area.

scholarly journals Existence and uniqueness of weak solutions of the Cauchy problem for parabolic delay-differential equations

1980 ◽  
Vol 21 (1) ◽  
pp. 65-80 ◽  
Author(s):  
S. Nababan ◽  
K.L. Teo
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Divergence Form ◽  
Partial Delay ◽  
The Cauchy Problem ◽  
Delay Differential

In this paper, a class of systems governed by second order linear parabolic partial delay-differential equations in “divergence form” with Cauchy conditions is considered. Existence and uniqueness of a weak solution is proved and its a priori estimate is established.

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