Vol 40, No 2 (2019)

By using fractional calculus and fixed point theorems, existence of mild solution for nonlinear Hilfer fractional integro-partial differential system is studied. In addition, sufficient conditions for controllability of Hilfer fractional integro-partial differential system is established.

It is considered the realization of k-valued logic functions (k = 4 and k = 5) by the circuits of unreliable functional elements in a complete basis consisting of the Webb function. It is assumed that the basis elements pass into faulty states independently of each other and the faults are such that each of the incorrect values appears at the output of the basis element with the same probability.

It is shown that any function of k-valued logic (k = 4 and k = 5) can be realized by the reliable circuit, the upper bound is obtained, and moreover the probability of the appearance of the fault is bounded by a constant.

In this present work we concern with mathematical modelling of biological experiments. The fractional hybrid iterative differential equations are suitable for mathematical modelling of biology and also interesting equations since the structure are rich with particular properties. The solution technique is based on the Dhage fixed point theorem that describes the mixed solutions by monotone iterative technique in the nonlinear analysis. In this method we combine two solutions, namely, lower and upper solutions. It is shown an approximate result for the hybrid fractional differential equations in the closed assembly formed by the lower and upper solutions.

This paper is aimed at constructing fractional power series (FPS) solutions of fractional Burgers-Huxley equations using residual power series method (RPSM). RPSM is combining Taylor’s formula series with residual error function. The solutions of our equation are computed in the form of rapidly convergent series with easily calculable components using Mathematica software package. Numerical simulations of the results are depicted through different graphical representations and tables showing that present scheme are reliable and powerful in finding the numerical solutions of fractional Burgers-Huxley equations. The numerical results reveal that the RPSM is very effective, convenient and quite accurate to time dependence kind of nonlinear equations. It is predicted that the RPSM can be found widely applicable in engineering.

The purpose of the paper is to study *-Ricci solitons and *-gradient Ricci solitons on three-dimensional normal almost contact metric manifolds. First, we prove that if a non-cosymplectic normal almost contact metric manifold with α, β = constant of dimension three admits a *-Ricci soliton, then the manifold is *-Ricci flat, provided β ≠ 0 and α ≠ ±β. Further, we prove that if a normal almost contact metric manifold with α, β = constant, of dimension three admits *-gradient Ricci soliton, then the manifold is *-Einstein, provided α² − β² ≠ 0.

In this article we propose to use special classes of the generalized functions in order to state the correct statement of some diffraction problems of electromagnetic waves by thin conducting screens in the cylindrical waveguides with conducting walls. As the generalized solutions, such mappings are considered which assign a linear functional defined on the linear shell of the set of the functions satisfying the corresponding boundary conditions to every value of longitudinal space coordinate. The traces of the solutions on the cross-section of the cylindrical domain are interpreted in the generalized sense. The infinite sets of linear algebraic equations are derived immediately from the generalized boundary conditions. We show that it is advisable to use the boundary conditions for the normal components of the electromagnetic field.

In this paper, we study singular fractional systems of nonlinear integro-differential equations. We investigate the existence and uniqueness of solutions by means of Schauder fixed point theorem and using the contraction mapping principle. Moreover, we define and study the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solutions. Some applications are presented to illustrate the main results.

We research an first initial-boundary value problem in a rectangular domain for a hyperbolic equation with Bessel operator. The solution of the problem depends on the numeric parameter in the equation. The solution is obtained in the form of the Fourier-Bessel series. There are proved theorems on uniqueness, existence and stability of the solution. The uniqueness of solution of the problem is established by means of the method of integral identities. And at the uniqueness proof are used completeness of the eigenfunction system of the spectral problem. At the existence proof are used assessment of coefficients of series, the asymptotic formula for Bessel function and asymptotic formula for eigenvalues. Sufficient conditions on the functions defining initial data of the problem are received.