Since the 60s of last century Fractional Calculus exhibited a remarkable progress and
presently it is recognized to be an important topic in the scientific arena. This survey …

In this paper we discuss a concept of dynamic memory and an application of fractional
calculus to describe the dynamic memory. The concept of memory is considered from the …

Transmutations, Singular and Fractional Differential Equations with Applications to
Mathematical Physics connects difficult problems with similar more simple ones. The book's …

In this chapter, we introduce notations, definitions, and preliminary facts that will be used in
the remainder of this book. Some notations and definitions from the fractional calculus, some …

The twentieth century was rich in great scientific discoveries. One of the most influential
events is the introduction of diffusion process, which has been widely used in physics …

We study the inverse problem of determining the right-hand side of a subdiffusion equation
with Riemann–Liouville fractional derivative whose elliptic part has the most general form …

The identification of the right order of the equation in applied fractional modeling plays an
important role. In this paper we consider an inverse problem for determining the order of …

The paper investigates an inverse problem for finding the order of the fractional derivative in
the sense of Gerasimov–Caputo in the wave equation with an arbitrary positive self-adjoint …

This is an advanced text on ordinary differential equations (ODEs) in Banach and more
general locally convex spaces, most notably ODEs on measures and various function …

The nonlocal boundary value problem, dt ρ u (t)+ A u (t)= f (t)(0< ρ< 1, 0< t≤ T), u (ξ)= α u
(0)+ φ (α is a constant and 0< ξ≤ T), in an arbitrary separable Hilbert space H with the …