EXTREMAL AND CONTINUA SOLUTIONS FOR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS

The aim of this work is to study two classes of stochastic fractional differential equations via the application of the method of upper and lower solutions combined with the Arzela-Ascoli theorem. We begin by proving an auxiliary result for the integral representation of an Airy-type stochastic problem. The specific symmetry features of an Airy-type stochastic problem depend on the form of the stochastic differential equations (SDE) and the relevant coefficients, it is vital to note. To comprehend each issue’s unique symmetries and their effects, a thorough investigation is necessary. Then, we prove an existence result for extremal solutions for the same problem. Another class of stochastic equations of higher-order type is also studied. We also present some examples to show the validity of the obtained results. At the end, a conclusion follows.