A New Representation for the Solutions of Fractional Differential Equations with Variable Coefficients

A recent development in differential equations with variable coefficients by means of fractional operators has been a method for obtaining an exact solution infinite series involving nested integral operators. This representation is constructive but difficult to calculate practice. Here, we show new the function, as convergent single integrals, which computationally simpler and believe will quickly prove its usefulness future computational work applications. In particular, constant coefficients, given Mittag-Leffler function. We also some applications Cauchy problems both time-fractional space-fractional time-dependent coefficients.