Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition

• Main Authors: M.M. El-Borai, K. El-S. El-Nadi, H.M. Ahmed, H. M. El-Owaidy, A.S. Ghanem, R. Sakthivel
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2018-01-01
• Series: Cogent Mathematics & Statistics
• Subjects: nonlinear fractional integro-partial differential equations; fractional brownian motion with hurst parameter less than half; nonlocal cauchy problem; stability
• Online Access: http://dx.doi.org/10.1080/25742558.2018.1460030

In this paper, a nonlinear fractional parabolic stochastic integro-partial differential equations with nonlocal effects driven by a fractional Brownian motion is considered. In particular, first we have formulated the suitable solution form for the fractional partial differential equations with nonlocal effects driven by fractional Brownian motion using a parabolic transform. Next, the existence and uniqueness of solutions are obtained for the fractional stochastic partial differential equations without any restrictions on the characteristic forms when the Hurst parameter of the fractional Brownian motion is less than half. Further, we investigate the stability of the solution for the considered problem. The required result is established by means of standard Picard’s iteration.