the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional mater...

In this paper, the wastewater treatment model is investigated by means of one most robust fractional derivatives, namely, Caputo derivative. The growth rate assumed to obey Contois model, which often used biomass in wastewaters. characteristics under consideration are derived and evaluated, such as equilibrium, stability analysis, steady-state solutions. Further, important allow us understand d...

In the present paper, concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo derivative. New results on existence and uniqueness are established by using theory operator semigroups, Hausdorff measure noncompactness, fixed point theorems calculus techniques. Applications a class fractional-order gene regulatory network (GRN) models propos...

Existence of solutions for a class of doubly nonlinear evolution equations of second order is proven by studying a full discretisation. The discretisation combines a time stepping on a nonuniform time grid, which generalises the well-known Störmer–Verlet scheme, with an internal approximation scheme. The linear operator acting on the zero-order term is supposed to induce an inner product, where...

In this paper, we propose the approximate solution of fractional diffusion equation described by a non-singular derivative. We use Atangana-Baleanu-Caputo derivative in our studies. The integral balance methods as heat method introduced Goodman and double developed Hristov have been used for getting solution. existence uniqueness provided. analyze impact operator process. represent graphically ...

We develop two topics in parallel and show their inter-relation. The first centers on the notion of a fractional-differentiable structure on a commutative or a non-commutative space. We call this study quantum harmonic analysis. The second concerns homotopy invariants for these spaces and is an aspect of non-commutative geometry. We study an algebra A, which will be a Banach algebra with unit, ...

The problems of unique solvability initial for linear inhomogeneous equations a general form with several Gerasimov-Caputo fractional derivatives in Banach spaces are investigated. Cauchy problem is considered an equation solved respect to the highest derivative containing bounded operators at lowest derivatives. solution presented use Dunford-Taylor type integrals. obtained result allowed us s...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...