On the sub–diffusion fractional initial value problem with time variable order

Abstract

We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

Keywords

• fractional derivative
• variable order
• regularity
• asymptotic behavior
• 34a08
• 34d05