The primary objective of this study is to examine the behavior of the nonlinear Kaup-Newell
equation. By employing the modified Kudryashov method and extended tanh function …

This study focuses on finding effective solutions to a mathematical equation known as the
Lonngren wave equation. The solutions from the Lonngren wave equation can be used to …

In this paper, we present the general Bernstein functions for the first time. The properties of
generalized Bernstein basis functions are given and demonstrated. The classical Bernstein …

In this paper, we employ the Caputo fractional derivative (CFD) approach and utilize the
truncated exponential method to tackle linear fractional optimal control problems (FOCPs) …

In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to
numerically solve both linear and nonlinear integro-differential equations with fractional …

In this manuscript, we adopt the Caputo fractional derivative approach and employ the
Galerkin-Bell method to tackle fractional optimal control problems (FOCPs) with equality and …

Purpose In this paper, the authors study the nonlinear matrix equation X p= Q±A (X-1+ B)-1
AT, that occurs in many applications such as in filtering, network systems, optimal control …

This paper presents two methods for solving two‐dimensional linear and nonlinear time‐
fractional advection–diffusion equations with Caputo fractional derivatives. To effectively …

The main feature of this paper is an application of the modified Bernstein operator in the
approximate and numerical solution of integral equations. The stability of the algorithm is …

In the present paper, the solvability and stability of a class of fractional Langevin equations
with integral and anti-periodic boundary conditions are considered. By applying the …