Sequential fractional differential equations with hadamard derivative

Citations of this article
Mendeley users who have this article in their library.
Get full text


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.




Klimek, M. (2011). Sequential fractional differential equations with hadamard derivative. Communications in Nonlinear Science and Numerical Simulation, 16(12), 4689–4697.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free