Numerical Solutions And Applications Of A Class Of Fractional-Order Stochastic Differential Equations

Some natural phenomena cannot be accurately described by integer derivatives due to their complexity,while fractional derivatives can be more flexible in the description of problems due to their memory,which helps us carry out research more widely.In addition,random interference is inevitable,and the consideration of random factors can make the description of the problem more real and accurate.In this paper,a class of stochastic differential equations with fractional derivatives of Ca-puto type is investigated.The fractional calculus,random analysis,and Picard's iteration are used to obtain the existence,uniqueness,stability and H¨older regularity of the solution of the equation,the nonlinear term is satisfied with some non-Lipschitz conditions?where the clas-sical Lipschitz conditions are special cases?.Using the Euler's method,the numerical scheme is constructed by approximating the term_?which is called white noise,and the term???is the derivative of the Brownian movement W?t?.Grownwall lemma is used to analyze the convergence and stability of the scheme,and the validity of the scheme is verified by numerical examples.The application of the model and method in Newton-Leipnik system and financial chaos system is also given.