Does the fractional derivative operator satisfy in a lipschitz or proper holder condition?

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Jorge Eliecer Hernandez Hernandez

May be in this book you can find what you are looking for:

Theory and Applications of Fractional Differential Equations, by Kilbas, A. A.; Srivastava, H. M.; and Trujillo, J. J. Amsterdam, Netherlands, Elsevier, Febrary 2006. ISBN 0-444-51832-0 (http://www.elsevier.com/wps/find/bookdescription.cws_home/707212/description#description)

Payam Mokhtary

Indeed i want to know that does the following inequality hold?

|D^a x-D^a y| < K|x-y|^m 0

You can check Theorem 3.15 of Chapter 3 of the book: The Analysis of Fractional Differential Equations, authored by K. Diethelm, and edited by Springer-Verlag Berlin Heidelberg in 2010.

Here I leave it.