Liang, Jin; Mu, Yunyi; Xiao, Ti-Jun Solutions to fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions. (English) Zbl 1427.34105 Banach J. Math. Anal. 13, No. 4, 745-768 (2019). Summary: We are concerned with fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions, where the operator pairs generate propagation families. With the help of the theory of propagation family and Laplace transforms, along with an estimate for a special sequence improved in this article, we introduce a definition of mild solutions to the impulsive problem for these abstract fractional Sobolev-type integro-differential equations and we establish general existence theorems and a continuous dependence theorem, which essentially extend some previous conclusions. In our results, the operator \(B\) could be unbounded, and the existence of an operator \(B^{-1}\) is not necessarily needed. Moreover, we give some examples to illustrate our main results. Cited in 5 Documents MSC: 34K37 Functional-differential equations with fractional derivatives 47D06 One-parameter semigroups and linear evolution equations 47N20 Applications of operator theory to differential and integral equations 34K30 Functional-differential equations in abstract spaces 34K45 Functional-differential equations with impulses 34K32 Implicit functional-differential equations Keywords:fractional integro-differential equations; Sobolev-type; operator pairs; propagation family × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] S. Abbas, M. Benchohra, and G. M. N’Guérékata, Topics in Fractional Differential Equations, Dev. Math. 27, Springer, New York, 2012. · Zbl 1273.35001 [2] S. Agarwal and D. Bahuguna, Existence of solutions to Sobolev-type partial neutral differential equations, J. Appl. Math. Stoch. Anal. 2006, no. 16308. · Zbl 1119.34060 [3] A. Aghajani, Y. Jalilian, and J. J. 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