Vol 40, No 2 (2019)
- Year: 2019
- Articles: 15
- URL: https://journals.rcsi.science/1995-0802/issue/view/12685
Article
Nonlinear Hilfer Fractional Integro-Partial Differential System
Abstract
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.
On the Vertical Similarly Homogeneous R-Trees
Abstract
We study the class of similarly homogeneous locally complete ℝ-trees with some additional requirements. In particular, vertical and strictly vertical ℝ-trees are defined. The metric classification of strictly vertical ℝ-trees is made: it is shown that every such ℝ-tree is isometric to some model ℝ-tree. For the vertical ℝ-trees which are not strictly vertical it is shown that their branching number is at least continuum.
Synthesis of Reliable Circuits in the Basis Consisting of the Webb Function in P4 and P5
Abstract
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.
A Note on Minimal Separating Function Sets
Abstract
We study point-separating function sets that are minimal with respect to the property of being separating. We first show that for a compact space X having a minimal separating function set in Cp(X) is equivalent to having a minimal separating collection of functionally open sets in X. We also identify a nice visual property of X2 that may be responsible for the existence of a minimal separating function family for X in Cp(X). We then discuss various questions and directions around the topic.
Mixed Solutions of Monotone Iterative Technique for Hybrid Fractional Differential Equations
Abstract
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.
A Note on Unbounded Generalized Multiplication Operators
Abstract
With the present paper, we attempt to describe the unbounded generalized multiplication operators, induced by some specific symbols, defined on the weighted Hardy spaces. We study their densely defined behavior and closedness together with the discussion of their normality and self-adjointness.
Analytical Solution of Fractional Burgers-Huxley Equations via Residual Power Series Method
Abstract
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.
Fixed Point Theorem for F-contraction Mappings, in Partial Metric Spaces
Abstract
The purpose of this paper is to establish a fixed point theorem for F-contraction mappings in partial metric spaces. Also, as a consequence, a fixed point theorem for a pair of F-contraction mappings having a unique common fixed point is obtained. In particular, the main results in this paper generalize and extend a fixed point theorem due to Wardowski 2012 in which F-contraction was introduced as a generalization of Banach Contraction Principle. An illustrative example is provided to validate the results.
*-Ricci Solitons on Three-dimensional Normal Almost Contact Metric Manifolds
Abstract
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.
On Generalized Solutions of Problems of Electromagnetic Wave Diffraction by Screens in the Closed Cylindrical Waveguides
Abstract
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.
Stability of Singular Fractional Systems of Nonlinear Integro-Differential Equations
Abstract
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.
On Inverse Boundary Value Problem for a Fredholm Integro-Differential Equation with Degenerate Kernel and Spectral Parameter
Abstract
In this paper are considered the questions of unique solvability and redefinitions of a nonlocal inverse problem for the Fredholm integro-differential equation of the second order with degenerate kernel, integral condition, and spectral parameter. Calculations of the value of the spectral parameter are reduced to the solve of trigonometric equations. Systems of algebraic equations are obtained. The singularities that arose in determining arbitrary constants are studied. A criterion for unique solvability of the problem is established and the corresponding theorem is proved.
First Initial-Boundary Value Problem for B-Hyperbolic Equation
Abstract
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.