Basic Theory of Fractional Differential Equations

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

“…There are three commonly used definitions of the fractional order differential operator, namely, Grunwald-Letnikov, Riemann-Liouville, and Caputo [12][13][14]. We use the fractional order system derived from the portal frame system (1) with the Grunwald -Letnikov (GL) definition, which is defined as…”

“…In this section we implement the proposed fractional order adaptive sliding mode controllers (FOASMC) derived in (23) along with the fractional parameter update laws (24) and sliding surfaces (13). For implementation of the entire control scheme we use Virtex 7 (Device: xc7vx980t-1ffg1926).…”

“…Recently many researchers have discussed fractional order calculus and its applications [12][13][14]. Fractional order nonlinear systems with different control approaches are investigated [15][16][17].…”

The method of lower and upper solutions for the general boundary value problems of fractional differential equations with p-Laplacian

“…In this paper, we study the fractional differential equation with p-Laplacian operators In recent years, the theory of fractional differential equations has become an important investigation area, see [1][2][3][4][5]. Many important results for certain boundary value conditions related to the fractional differential equations had been obtained, for example, twopoint boundary value problem, multi-point boundary value problem, integral boundary value problem and so on, see [6][7][8][9][10][11][12][13][14][15][16].…”

Forced Oscillation of Solutions of a Fractional Neutral Partial Functional Differential Equation

“…order and have gained considerable importance due to the fact that these equations are applied in real world problems arising in various branches of science and technology [1]- [5]. Neutral delay differential equations have applications in electric networks containing Lossless transmission lines and population dynamics [6].…”