numerical solution of fractional stochastic differential equations and stability analysis

In this paper, we investigate the exponential mean square stability for boththe solution of variable order fractional stochastic differential equations (fsdes) withpoisson jump, as well for the compensated milstein scheme implemented of the proposedmodel. first, we prove that the considered model has the property of exponential meansquare stability. moreover, it is shown that the compensated milstein scheme can inheritthe exponential mean square stability by using the variable order fractional stochasticdifferential equations with poisson jump in the paper. eventually, numerical solutionare provided to show the effectiveness of the theoretical results. also, by introducing thecompensated milstein scheme and by using some numerical integration technique as wellapproximating the integro part of the model by the simple trapezoidal rule, we obtain thesame exponential mean square stability property for some restrictive stepsizes. finally,we proved the exponential mean square stability by using the compensated milsteinmethod