Existence of solutions for the (p,q)-Laplacian equation with nonlocal Choquard reaction

Solving the Fornberg–Whitham Model Derived from Gilson–Pickering Equations by Analytical Methods

“…Researchers have focused on finding the analytical or exact solutions to problems which contributes to the analysis of the actual system characteristics. A number of years ago, different efficient and significant methods were developed to obtain solutions, including: the trial equation method, the modified trial equation method [1], the direct algebraic method, the Sine-Gordon expansion method [2], the first integral method, the functional variable method [3], the rational (G ′ /G 2 )-expansion method [4,5], the Nucci's reduction method, the extended hyperbolic method [6], the generalized invariant subspace method [7], the new Kudryashov approach [8], and many others [9][10][11][12][13][14][15].…”

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

“…Super symmetry is a symmetry that relates particles with different spins and has important implications for studying fundamental particles. In summary, investigating the impact of fractional non-linearity in the Klein-Gordon equation on quantum dynamics and the connection between symmetry is an active area of research that has important implications for theoretical and experimental physics [27][28][29][30][31].…”

An algorithm for solution of the Sylvester s‐conjugate linear equation for the commutative elliptic octonions

“…The solutions of the linear equation systems are ubiquitous in essentially all quantitative areas of human endeavor, including industry and science. Linear equation systems play an important role in the areas of such as linear algebra in Choguard reaction systems [1], pattern formation [2], Keller–Segel systems [3, 4], computer science, mathematical computing, optimization, signal processing, engineering, numerical analysis, computer vision, many applications of control theory, and machine learning [5–10]. Sylvester linear equation, which is the most important one of these linear equations, has many uses such as control system, stability, eigenstructure assignment, pole assignment, and observer design (e.g., [11–15] Bevis, Hall and Hartwig [16]) that have studied the equation $$$$ A\overline{X}- XB=C $$$$ known as the Sylvester‐conjugate equation where $$$ A $$$ and $$$ B $$$ are complex $$$ m\times m $$$ and $$$ n\times n $$$ matrices, respectively, and $$$ \overline{X} $$$ denotes the matrix obtained by taking the complex conjugate of each element of $$$ X\in {\mathrm{\mathbb{C}}}^{m\times n} $$$.…”

“…The solutions of the linear equation systems are ubiquitous in essentially all quantitative areas of human endeavor, including industry and science. Linear equation systems play an important role in the areas of such as linear algebra in Choguard reaction systems [1], pattern formation [2], Keller-Segel systems [3,4], computer science, mathematical computing, optimization, signal processing, engineering, numerical analysis, computer vision, many applications of control theory, and machine learning [5][6][7][8][9][10]. Sylvester linear equation, which is the most important one of these linear equations, has many uses such as control system, stability, eigenstructure assignment, pole assignment, and observer design (e.g., [11][12][13][14][15] Bevis, Hall and Hartwig [16]) that have studied the equation…”