Existence uniqueness of mild solutions for \(\psi \)-Caputo fractional stochastic evolution equations driven by fBm. (English) Zbl 1504.35629
Summary: In this paper, we investigate the existence uniqueness of mild solutions for a class of \(\psi \)-Caputo fractional stochastic evolution equations with varying-time delay driven by fBm, which seems to be the first theoretical result of the \(\psi \)-Caputo fractional stochastic evolution equations. Alternative conditions to guarantee the existence uniqueness of mild solutions are obtained using fractional calculus, stochastic analysis, fixed point technique, and noncompact measure method. Moreover, an example is presented to illustrate the effectiveness and feasibility of the obtained abstract results.
MSC:
| 35R11 | Fractional partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 26A33 | Fractional derivatives and integrals |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
\(\psi\)-Caputo fractional derivative; stochastic evolution equations; noncompact measure; fractional Brownian motionReferences:
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