Existence results for an impulsive fractional integro-differential equation with state-dependent delay. (English) Zbl 1410.34242
Summary: In this paper, we have a tendency to implement different fixed point theorem [ Banach contraction principle, Krasnoselskii’s [J. Dabas et al., Int. J. Differ. Equ. 2011, Article ID 793023, 20 p. (2011; Zbl 1239.34094)] and Schaefer’s [Dabas et al., loc. cit.] coupled with solution operator to analyze the existence and uniqueness results for an impulsive fractional integro-differential equations (IFIDE) with state-dependent delay (SDD) in Banach spaces. Finally, cases are offered to demonstrate the concept.
MSC:
| 34K45 | Functional-differential equations with impulses |
| 34A08 | Fractional ordinary differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
| 35R11 | Fractional partial differential equations |
| 35R12 | Impulsive partial differential equations |
| 45J05 | Integro-ordinary differential equations |
Keywords:
fractional order differential equations; impulsive conditions; state-dependent delay; fixed point theorems; semigroup theoryCitations:
Zbl 1239.34094References:
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