The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...

The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order β ∈ (0, 1) . The fundamental solution for the Cauchy problem is interpreted as a probability density of a selfsimilar non-Markovian stochastic process related to a phenomenon of subdiffusion (the variance grows in time sub-lin...

It is well-known that the construction of space of probability measures P is functorial in the category Comp of compact Hausdorff spaces. The functor P is normal in the sense of E.V. Shchepin [1]. It is well-known that the functor P is open, i.e. it preserves the class of open surjective maps. This was first proved by Ditor and Eifler [2]. E.V. Shchepin [1] discovered tight relations between th...