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. © 2011 Elsevier B.V.