In this paper based on a system of Riccati equations with variable coefficients, we presented a new Riccati equation with variable coefficients expansion method and its algorithm, which are direct and more powerful than the tanh-function method, sine-cosine method, the generalized hyperbolic-function method and the generalized Riccat equation with constant coefficient expansion method to constr...

In this study the radial part of the Schrödinger equation in presence of the angular momentum (l 6= 0) has been solved for the generalized Woods-Saxon potential by using the modification method. This approach is based on the definition of a modified Woods-Saxon potential which is selected that the associated Schrödinger differential equation become comparable with the associated Jacobi differen...

An efficient computational method is presented for state space analysis of singular systems via Haar wavelets. Singular systems are those in which dynamics are governed by a combination of algebraic and differential equations. The corresponding differential-algebraic matrix equation is converted to a generalized Sylvester matrix equation by using Haar wavelet basis. First, an explicit expressio...

The joint distribution of a geometric Brownian motion and its time-integral was derived in seminal paper by Yor (1992) using Lamperti’s transformation, leading to explicit solutions terms modified Bessel functions. In this paper, we revisit classic result the simple Laplace transform approach connection Heun differential equation. We extend methodology with affine drift show that process can be...

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furtherm...

We use the improved general mapping deformationmethod based on the generalized Jacobi elliptic functions expansionmethod to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi ellipt...

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

We study the finite-temperature deformation of discrete Bessel point process. show that its largest particle distribution satisfies a reduction 2D Toda equation, as well version integro-differential Painlev\'e II equation Amir-Corwin-Quastel, and we compute initial conditions for Poissonization parameter equal to 0. As proved by Betea Bouttier, in suitable continuum limit last converges Airy re...