Binary simplest equation method to the generalized Sinh–Gordon equation

On the explicit solutions of fractional Bagley-Torvik equation arises in engineering

“…A fractional mathematical model for a micro-electro-mechanical system (MEMS) device has been developed to measure the viscosity of fluids during oil well exploration by Fitt et al [15]. There are many numerical methods based on Bernoulli polynomials [11], generalized form of the Bessel functions of the first kind [9], wavelet [10], the generalized Taylor series [8], spline methods [17,18], finite difference scheme [12,16] [32][33][34][35], transformed rational function method [37], multiple exp-function method [38]. Besides different approaches to solve fractional partial differential equation, the other most important tool is defination of the fractional derivative.…”

New fractional calculus and application to the fractional-order of extended biological population model

“…Among the investigations for fractional differential equations, research into seeking exact solutions and numerical solutions of fractional differential equations is an important topic. Many powerful and efficient methods have been proposed to obtain numerical solutions and exact solutions of fractional differential equations [1][2][3] and [13][14][15][16][17][18][19][20][21][22][23]. Recently, a new modification of Riemann-Liouville derivative is proposed by Jumarie [4,7]:…”