An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation

Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

“…To find the answer of this question, the mathematicians have managed to open a new window of opportunities to improve the mathematical modeling of real world problems, which has given birth to many new questions and intriguing results. These newly established results have numerous implementation in many areas of engineering [1,2], such as fractional-order Buck master and diffusion problems [3], fractional-order telegraph model [4,5], fractional KdV-Burger-Kuramoto equation [6], fractal vehicular traffic flow [7], fractional Drinfeld-Sokolov-Wilson equation [8], fractional-order anomalous sub-diffusion model [9], fractional design of hepatitis B virus [10], fractional modeling chickenpox disease [11], fractional blood ethanol concentration model [12], fractional model for tuberculosis [13], fractional vibration equation [14], fractional Black-Scholes option pricing equations [15], fractionally damped beams [16], fractionally damped coupled system [17], fractional-order heat, wave and diffusion equations [18,19], fractional order pine wilt disease model [20], fractional diabetes model [21] etc.…”

Solution of nonlinear differential equation and special functions

“…In recent years, it has been observed that nonlinear differential equations find their applications in physics and engineering. Several authors have paid their attention in this special branch of applied mathematics such as Sharma, 1 Saxena and Kushwaha, 2 Garde, 3 Srivastava, 4 Srivastava and Singh 5 Kumar et al, 6,7 Singh et al, 8 Singh et al, 9,10 and Bansal et al 11,12 The nonlinear differential equations and their solutions are very important to study the various scientific processes. Therefore, in the present work, we apply the Hermite, Legendre, and Jacobi polynomials and their linear approximation to obtain the approximate solution of the following general nonlinear differential equations:…”

Numerical analysis for Klein‐Gordon equation with time‐space fractional derivatives

“…It is worth mentioning that the numerical method of fractional order equation is reported in the existing work. [13][14][15][16][17][18][19] Golmankhaneh et al 20 presented homotopy perturbation method to investigate analytical solutions for the fractional Klein-Gordon equation. Gepreel et al 21 On the other hand, many research works have been done on efficient numerical scheme for space-fractional equations.…”