A note on the fractional hyperbolic differential and difference equations

Positive Solutions for a System of Fractional Differential Equations with Nonlocal Integral Boundary Conditions

“…It is shown that the mean advantages of fractional order derivatives and integrals is their ability to describe memory and hereditary properties of different materials, for more details see [1][2][3]. Let us note that there exists abundant literature concerning the relation between fractional derivatives and fractional powers of operators [4,5], fractional partial differential equations [6] and boundary value problems involving fractional calculus [7][8][9][10][11][12][13].…”

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

“…The papers on the modelling physical phenomena via fractional Bagley-Torvik equation, the numeric [8][9][10][11][12] or analytical solutions [6,13,14] of Eq. (1) are seen in the literature commonly.…”

“…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.…”

A note on fractional parabolic differential and difference equations

“…Theory and numerical methods of initial-boundary value problems for fractional parabolic equations were investigated by many researchers (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][22][23][24] and the references given therein). In this paper, the initial-boundary value problem for the multidimensional fractional parabolic equation…”