Resumen de Stochastic Averaging of Non-linear Implicit Caputo’s Fractional Differential Equation with Multiplicative Fractional Brownian Motion
Manzoor Ahmad, Akbar Zada, Sana Ben Moussa, Afef Kallekh, Mohammad Esmael Samei
In contrast to the previous research for various type of stochastic Caputo’s fractional differential equations, we establish an averaging principle for a non-linear stochastic implicit Caputo’s fractional differential equation with fractional Brownian motion as its driving force. Under appropriate conditions, we demonstrate that the mild solution of the original equation is approximately equivalent to that of the reduced averaged equation. The obtained convergence result guarantees that one can study the complex system through the simplified system. We establish the validity of our result through mean square by utilizing Hölder inequality and growth bounds for the equation in considered model. Better yet, our techniques can be applied to improve some existing results. As for application, one example is worked out to explain the procedure and validity of the proposed averaging principles.
