ON THE PROBABILISTIC APPROACH TO THE SOLUTION OF GENERALIZED FRACTIONAL DIFFERENTIAL EQUATIONS OF CAPUTO AND RIEMANN-LIOUVILLE TYPE M. E. HERN ANDEZ-HERNANDEZ, V. N. KOLOKOLTSOV

Document Type : Regular research papers

Abstract

This paper provides a probabilistic approach to solve linear equa tions involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we obtain well-posedness results and explicit solutions (in terms of the transition densities of the underlying stochastic processes). The problems studied here include fractional linear differential equations, well analyzed in the literature, as well as their far reaching extensions.

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