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This paper studies a fractional nonlocal stochastic differential equation of Sobolev type in a separable Hilbert space. The sufficient conditions for the existence of a mild solution to the Sobolev type fractional stochastic differential equation with nonlocal conditions are obtained by using the Schauder fixed point theorem and approximating techniques under the assumption that the nonlinear part and nonlocal term satisfy some local growth conditions. An example is provided for applicability of the main results.
How to Cite this Article:
Alka Chadha, D.N. Pandey, Dhirendra Bahuguna, Existence of a mild solution for Sobolev type stochastic fractional differential equations with nonlocal conditions, Journal of Nonlinear Functional Analysis 2016 (2016), Article ID 23.