In economics, depreciation functions (operator kernels) are certain decreasing functions, which assumed to be equal unity at zero. Usually, an exponential function is used as a function. However, in operator kernels do not allow simultaneous consideration of memory effects and effects. this paper, it proposed consider non-exponential type, simultaneously take into account by using the Prabhakar...

We prove a Liouville-type theorem for bounded stable solutions v ∈ C(R) of elliptic equations of the type (−∆)v = f(v) in R, where s ∈ (0, 1) and f is any nonnegative function. The operator (−∆) stands for the fractional Laplacian, a pseudo-differential operator of symbol |ξ|.

and Applied Analysis 3 where n α 1, α denotes the integer part of number α, provided that the right side is pointwise defined on 0, ∞ . Definition 2.2 see 20 . The Riemann-Liouville fractional integral of order α > 0 of a function f : 0, ∞ → R is given by I 0 f t 1 Γ α ∫ t 0 t − s α−1f s ds, 2.2 provided that the right side is pointwise defined on 0, ∞ . From the definition of the Riemann-Liouv...

We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.

<p>This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating Riemann-Liouville fractional derivative operator. These are derived by utilizing forthright computations, so-called weighted mean value theorem (WMVT). Undoubtedly, such will be extremely useful establishing approaches several ...

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized f...

The continuity for some multilinear operators related to certain fractional singular integral operators on Triebel-Lizorkin spaces is obtained. The operators include Calderon-Zygmund singular integral operator and fractional integral operator. 1. Introduction. Let T be a Calderon-Zygmund singular integral operator; a well-known result of Coifman et al. (see [6]) states that the commutator [b, T...