Sequential fractional differential equations with Hadamard derivative

Abstract

A class of nonlinear sequential fractional differential equations dependent on the basic fractional operator involving a Hadamard derivative is studied for arbitrary real noninteger order α ∈ R + . The existence and uniqueness of the solution is proved using the contraction principle and a new, equivalent norm and metric, introduced in the paper. As an example, a linear nonhomogeneous FDE is solved explicitly in arbitrary interval [ a, b] and for a nonhomogeneous term given as an arbitrary Fox function. The general solution consists of the solution of a homogeneous counterpart equation and a particular solution corresponding to the nonhomogeneous term and is given as a linear combination of the respective Fox functions series.