Well-posedness and regularity for solutions of caputo stochastic fractional differential equations in Lp spaces

Abstract

Abstract In the first part of this paper, we establish the well-posedness for solutions of Caputo stochastic fractional differential equations (for short Caputo SFDE) of order in Lp spaces with whose coefficients satisfy a standard Lipschitz condition. More precisely, we first show a result on the existence and uniqueness of solutions, next we show the continuous dependence of solutions on the initial values and on the fractional exponent α. The second part of this paper is devoted to studying the regularity in time for solutions of Caputo SFDE. As a consequence, we obtain that a solution of Caputo SFDE has a δ-Hölder continuous version for any The main ingredient in the proof is to use a temporally weighted norm and the Burkholder-Davis-Gundy inequality.