A blowup alternative result for fractional nonautonomous evolution equation of Volterra type
By Pengyu Chen, Xuping Zhang, Yongxiang Li. 2018
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In this article, we consider a class of fractional non-autonomous integro-differential evolution equation of Volterra type in a Banach space \begin{document}$E$\end{document} , where the operators in linear part (possibly unbounded) depend on time \begin{document}$t$\end{document} . Combining the theory of fractional calculus, operator semigroups and measure of noncompactness with Sadovskii's fixed point theorem, we firstly proved the local existence of mild solutions for corresponding fractional non-autonomous integro-differential evolution equation. Based on the local existence result and a piecewise extended method, we obtained a blowup alternative result for fractional non-autonomous integro-differential evolution equation of Volterra type. Finally, as a sample of application, these results are applied to a time fractional non-autonomous partial integro-differential equation of Volterra type with homogeneous Dirichlet boundary condition. This paper is a continuation of Heard and Rakin [ 13 , J. Differential Equations, 1988] and the results obtained essentially improve and extend some related conclusions in this area.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/725e397c514d8abd5a531fe0da8b2e938607fb0c
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In Applied Mathematics
In Modeling and Simulation
Citations in the corpus
- Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families (2021, background): “On the other hand, non-autonomous evolution equations have been extensively studied in recent years using various fixed point theorems when the corresponding evolution family is compact, see for example [3, 9, 11, 12, 13, 17, 18, 23, 35, 36], this is very convenient to the equations with compact res”
- Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators (2020, background): “Since fractional order semilinear evolution equations are abstract formulations for many problems arising in engineering and physics, fractional evolution equations have attracted a large amount of attention in recent years, see [9, 13, 14, 15, 17, 19, 22, 23, 27, 28, 40, 41, 43, 44, 45, 48, 51] and”