Variable order block backward differentiation formulae (VOHOBBDF) method is employed for treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) o...
A theory for the calculation of the phase–lag and amplification–factor for explicit and implicit multistep techniques for first–order differential equations was recently established by the author. His presentation also covered how t...
This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula (...
This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann...
It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas. Using discrete analogs of differential operators, optimal interpolation, quadrature, and differe...
In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6)), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consis...
In the present study, we use several identities from the q-calculus to define the concept of q-Hermite polynomials with three variables and present their associated formalism. Many properties and new results of q-Hermite polynomials of three variable...
In this study, a singly diagonally implicit block backward differentiation formula (SDIBBDF) was proposed to approximate solutions for a dynamical HIV infection model of CD 4 + T cells. A SDIBBDF method was developed to overcome difficulty when...
In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establis...
A computational approach with the aid of the Linear Multistep Method (LMM) for the numerical solution of differential equations with initial value problems or boundary conditions has appeared several times in the literature due to its good accuracy a...
Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of v...
The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics. Specifically, the formula provides a solution to the part...
This article deals with the general linearization problem of Jacobi polynomials. We provide two approaches for finding closed analytical forms of the linearization coefficients of these polynomials. The first approach is built on establishing a new f...
This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of orde...
Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in...
In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable an...
This work is devoted to the obtaining of a new numerical scheme based on quadrature formulae for the Lebesgue–Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically appr...
Infant formulas (IFs) are prevalent alternatives for human milk (HM), although their comparative lipid profiles have not been fully investigated. We adopted lipidomics to analyze and compare in-depth the lipid patterns of HM and IFs. The results indi...
Based upon a new general vector-valued vector product, generalized complex numbers with respect to certain positively homogeneous functionals including norms and antinorms are introduced and a vector-valued Euler type formula for them is derived usin...
In this paper, we introduce and study new features for 2-variable (p,q)-Hermite polynomials, such as the (p,q)-diffusion equation, (p,q)-differential formula and integral representations. In addition, we establish some summation models and their (p,q...
In the Middle East, there remain many technical challenges in the water saturation evaluation of carbonate rocks and the effective identification of reservoir fluid properties. The traditional Archie equation is not applicable to carbonate reservoirs...
In the paper, by virtue of a derivative formula for the ratio of two differentiable functions and with the help of a monotonicity rule, the authors expand a logarithmic expression involving the sine function into the Maclaurin power series in terms o...
The correct evaluation of the curvatures of ball screw grooves allows the accurate design of the constructive parameters of this mechanism and enhancing its performance. The formulation commonly used in the literature, however, refers to ball bearing...
This manuscript introduces the family of Gould–Hopper–Lambda polynomials and establishes their quasi-monomial properties through the umbral method. This approach serves as a powerful mechanism to analyze the characteristic of multi-variab...
In this paper, we obtain the existence, uniqueness, and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market and the Bla...
This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). U...
This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics. By using the Dynkin formula and solution of the Dirichlet&nd...
In this study, two numerical schemes with second-order accuracy in time for a modified Ericksen–Leslie model are constructed. The highlight is based on a novel convex splitting method for dealing with the nonlinear potentials, which is integrat...
In this paper, our primary objective is to develop a robust and efficient higher-order structure-preserving algorithm for the numerical solution of the two-dimensional nonlinear spatial fractional Schrödinger equation. This equation, which incor...
In order to study the residual strength of buried pipelines with internal corrosion defects in seasonally frozen soil regions, we established a thermo-mechanical coupling model of a buried pipeline under differential frost heave by using the finite e...
In this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues’ formula, several recurrence relations including three-term rela...
Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in...
This paper introduces a novel collocation scheme based on an extended cubic B-spline for approximating the solution of a second-order partial integro-differential equation. The proposed scheme employs new extended cubic B-splines to discretize the se...
In this paper, we focus on investigating the well-posedness of backward stochastic differential equations with jumps (BSDEJs) driven by irregular coefficients. We establish new results regarding the existence and uniqueness of solutions for a specifi...
We focus on solving stochastic differential equations driven by jump processes (SDEJs) with measurable drifts that may exhibit quadratic growth. Our approach leverages a space transformation and Itô-Krylov’s formula to effectively elimina...
Composite integral formulas offer greater accuracy by dividing the interval into smaller subintervals, which better capture the local behavior of function. In the finite volume method for solving differential equations, composite formulas are mostly...
The main contribution in this paper is to construct an implicit fixed coefficient Block Backward Differentiation Formulas denoted as A ( α ) -BBDF with equal intervals for solving stiff ordinary differential equations (ODEs). To avoid...
In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal d...
Differential Scanning Calorimetry (DSC) is a regular and powerful tool to measure the specific heat profile of various materials. In order to connect the measured profile to the properties of a particular protein, a model is required to fit. We discu...
Many authors have established various integral and differential formulas involving different special functions in recent years. In continuation, we explore some image formulas associated with the product of Srivastava’s polynomials and extended...
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,...
From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we...
In applications, many states given for a system can be expressed by orthonormal elements, called “state elements”, taken in a separable Hilbert space (called “state space”). The exact nature of the Hilbert space depends on the system; for example, th...
The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) and stochastic differential equations (SDEs) to a wider class of stochastic processes, including fractional Brownian motions...
In this paper, we promote the refinement method for estimating asymptotic expression of the fundamental solutions of a fourth order linear differential equation with discontinuous weight function and transmission conditions. These refinement solution...
Applying the operator of q-difference, we examine the convolution properties of the subclasses MSζ,qr,p(A,B) and MKζ,qr,p(A,B) of p-valent meromorphic functions defined in the punctured open-unit disc. We derived specific inclusion features...
This paper extends the idea of subordination from the theory of fuzzy sets to the geometry theory of analytic functions with a single complex variable. The purpose of this work is to define fuzzy subordination and illustrate its main characteristics....
The topic concerning the introduction and investigation of new classes of analytic functions using subordination techniques for obtaining certain geometric properties alongside coefficient estimates and inclusion relations is enriched by the results...
This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag...
Several integrability problems of differential equations are addressed using the concept of a C∞-structure, a recent generalization of the notion of solvable structure. Specifically, the integration procedure associated with C∞-structures...
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