Partial Functional Evolution Equations with Finite Delay

2015 ◽  
pp. 17-45
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Evolution Equations ◽  
Functional Evolution ◽  
Finite Delay

scholarly journals On a study of Sobolev type fractional functional evolution equations

2021 ◽  
Author(s):  
Ismail T. Huseynov ◽  
Arzu Ahmadova ◽  
Nazim Mahmudov
Keyword(s):  
Time Delay ◽  
Evolution Equations ◽  
Delay System ◽  
Analytical Representation ◽  
Sobolev Type ◽  
Bounded Operators ◽  
Functional Evolution ◽  
Representation Of Solutions ◽  
The Given ◽  
Fractional Functional

Sobolev type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate fractional-order time-delay evolution equation of Sobolev type with multi-orders in a Banach space and introduce an analytical representation of a mild solution via a new delayed Mittag-Leffler type function which is generated by linear bounded operators. Furthermore, we derive an exact analytical representation of solutions for multi-dimensional fractional functional dynamical systems with nonpermutable and permutable matrices. We also study stability analysis of the given time-delay system in Ulam-Hyers sense with the help of Laplace transform.

scholarly journals Second order quasilinear functional evolution equations

2015 ◽  
Vol 140 (2) ◽  
pp. 139-152
Author(s):  
László Simon
Keyword(s):  
Evolution Equations ◽  
Second Order ◽  
Functional Evolution

scholarly journals Controllability of Second-Order Semilinear Impulsive Stochastic Neutral Functional Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lei Zhang ◽  
Yongsheng Ding ◽  
Tong Wang ◽  
Liangjian Hu ◽  
Kuangrong Hao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Functional Evolution ◽  
Cosine Families ◽  
Families Of Operators ◽  
Sadovskii Fixed Point Theorem ◽  
Stochastic Functional

We consider a class of impulsive neutral second-order stochastic functional evolution equations. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. An example is provided to illustrate our results.

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