We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

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In this article, fractional exponential operator is considered as a general approach for solving partial fractional differential equations. An integral representation for this operator is derived from the Bromwich integral for the inverse Mellin transform. Also, effectiveness of this operator for obtaining the formal solution of system of diffusion equations is discussed.

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