A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

Let dγ(x) ≡ πe 2 dx for all x ∈ R be the Gauss measure on R. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L(γ) to L(γ), or from the...

Based on the Riemannand Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed derivative types. An analytic extended symmetric rotor model is derived, which correctly predicts the sequence of magic numbers in metal clusters. It is demonstrated...

The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting two elements that are described by fractional derivatives different orders. These designed performed as RC ladders with properly selected values resistances capacitances. Different orders differentiation lead state-space system model, in which each state variable has a order derivative. Solutions...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all real line by quasi-interpolation neural network operators. These approximations are derived establishing Jackson type inequalities involving modulus continuity engaged function its high order derivative fractional derivatives. Our operator...