In this paper, a generalized nonlinear Schrödinger (gNLS) equation with time-varying coefficients is analytically studied using its Lax representation and the associated Riemann-Hilbert (RH) problem equipped with a symmetric scattering matrix in...
We consider a Cauchy problem for the inhomogeneous differential equation given in terms of an unbounded linear operator A and the Caputo fractional derivative of order α∈(0,2) in time. The previously known representation of the mild soluti...
This paper is devoted to the general theory of systems of linear time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order is k...
Water distribution networks (WDNs) are vital for communities, facing threats like climate change and aging infrastructure. Optimizing WDNs for energy and water savings is challenging due to their complexity. In particular, pump scheduling stands out...
For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula,...
Solutions to the Davey–Stewartson equations (DS) in terms of the determinants of order 2N depending on 4N real parameters are constructed. The Darboux transformation is used to construct solutions of order N to this equation. We obtain a repres...
In this paper, we present certain complete solutions in the dilatation theory of elasticity. This model can be derived as a special case of Eringen’s linear theory of microstretched elastic solids when microrotations are absent. It is also a ve...
In the present paper, first we obtain sufficient conditions for the existence and uniqueness of the solution of the Cauchy problem for an inhomogeneous neutral linear fractional differential system with distributed delays (even in the neutral part) a...
In this paper, we give the necessary and sufficient conditions for the existence of general solutions, self-adjoint solutions, and positive solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2) under additional conditions. In addition, we derive the...
The aim of this work is to obtain an integral representation formula for the solutions of initial value problems for autonomous linear fractional neutral systems with Caputo type derivatives and distributed delays. The results obtained improve and ex...
A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the f...
This paper investigates linear two-sided fractional matrix delay differential equations (TSFMDDE). Firstly, the two-sided fractional delayed Mittag-Leffler matrix functions (TSFDMLMF) are constructed. Further, the representation of solutions of two-s...
In this work, we study a general class of retarded linear systems with distributed delays and variable-order fractional derivatives of Caputo type. We propose an approach consisting of finding an associated one-parameter family of constant-order frac...
The efficient solution (fast and accurate) of parametric partial differential equations (pPDE) is of major interest in many domains of science and engineering, enabling evaluations of the quantities of interest, optimization, control, and uncertainty...
In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the...
The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classica...
The paper studies a class of nonlinear disturbed neutral linear fractional systems with derivatives in the the Riemann–Liouville sense and distributed delays. First, it is proved that the initial problem for these systems with discontinuous ini...
Background: The benefit of hearing rehabilitation is often measured using audiological tests or subjective questionnaires/interviews. It is important to consider both aspects in order to evaluate the overall benefits. Currently, there is no standardi...
In this paper, we propose a definition of block tensors and the real representation of tensors. Equipped with the simplification method, i.e., the real representation along with the M-P inverse, we demonstrate the conditions that are necessary and su...
In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations over the ge...
In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB = C, and present the general solution expression when the solvability conditions are met. As an application, we de...
In this paper a nonlinear system of Riemann–Liouville (RL) fractional differential equations with non-instantaneous impulses is studied. The presence of non-instantaneous impulses require appropriate definitions of impulsive conditions and init...
In this paper, we investigate a delayed matrix exponential and utilize it to derive a representation of solutions to a linear nonsingular delay problem with permutable matrices. To begin with, we present a novel definition of α-exponential stab...
We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expa...
This paper addresses the solvability and controllability of fractional delay differential Sylvester matrix equations with non-permutable coefficient matrices. By applying a vectorization approach and Kronecker product algebra, we transform the matrix...
A three-dimensional survey of natural caves is often a difficult task due to the roughness of the investigated area and the problems of accessibility. Traditional adopted techniques allow a simplified acquisition of the topography of caves characteri...
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a d-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism...
Business process models help to visualize processes of an organization. In enterprises, these processes are often specified in internal regulations, resolutions or other law acts of a company. Such descriptions, like task lists, have mostly form of e...
A dynamic uncertain causality graph (DUCG) is a probabilistic graphical model for knowledge representation and reasoning, which has been widely used in many areas, such as probabilistic safety assessment, medical diagnosis, and fault diagnosis. Howev...
The fundamentals of discontinuous precipitation (DP) reaction modelling using a cellular automata (CA) method are presented. In the proposed CA model, cell states, internal variables, equations, and transition rules were defined to predict the manner...
Number sequences are among the research areas of interest in both number theory and linear algebra. In particular, the study of matrix representations of recursive sequences is important in revealing the structural properties of these sequences. In t...
With a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation as well as the multiple Darboux transformation, which enables the obtainment of compact solutions of this equati...
The work defines in a new way the different types of solutions of the inverse kinematics (IK) problem for planar robots with a serial topology and presents an algorithm for solving it. The developed algorithm allows the finding of solutions for a wid...
From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection betw...
Firstly, a basic question to find the Laplace transform using the classical representation of gamma function makes no sense because the singularity at the origin nurtures so rapidly that Γze−sz cannot be integrated over positive real numb...
Recognizing construction workers’ activities is essential for effective construction management. The complexity of construction sites and the varied, dynamic nature of workers’ actions make automatic monitoring of their behaviors challeng...
Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we pr...
Nonlinear evolution equations play a key role in modeling various physical processes, such as wave propagation in nonlinear optical and hydrodynamic media, as well as in the dynamics of plasma and quantum systems. In this paper, we study an integrabl...
The description of the Earth’s gravitational field, governed by the fundamental potential equation (the Laplace equation), is conventionally expressed using spherical harmonics, yet the Cartesian formulation, using a Taylor series representatio...
In the previous author’s works, a representation of the solution of the Dirichlet boundary value problem for the biharmonic equation in terms of Green’s function is found, and then it is shown that this representation for a ball can be written in the...
In this paper, based on a new representation of the Green’s function of the Navier problem for the 3-harmonic equation in the unit ball, an integral representation of the solution of the corresponding Navier problem is found. Then, for the Navi...
Representation in mathematics is essential as a basis for students to be able to understand and apply mathematical ideas. This study aims to describe how students produce different representations in solving word problems. In solving word problems, s...
The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes, discrete polymatroids, which can...
In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equ...
The fundamental solution to the multi-dimensional space-time fractional diffusion equation is studied by applying the subordination principle, which provides a relation to the classical Gaussian function. Integral representations in terms of Mittag-L...
A method of the Riemann–Hilbert problem is applied for Zhang’s conjecture 1 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in the zero external field and the solution to the Zhang’s conjecture 1 is const...
Our study focuses on the governing equation of a finitely deformed flexible rod with strain waves. By utilizing the well-known Ablowita–Ramani–Segur (ARS) algorithm, we prove that the equation is non-integrable in the Painlevé sens...
Although describing very different physical systems, both the Klein–Gordon equation for tachyons (m2<0) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a sui...
In the current contribution, integral representations of the solutions of homogeneous and nonhomogeneous delay differential equation of a fractional Hilfer derivative are established in terms of the delayed Mittag-Leffler-type matrix function of two...
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the originally developed noncommutative integration method for linear partial differential equations. The application of the method is based on the symmetry pr...
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