Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation

On the numerical solution of space fractional order diffusion equation via shifted Chebyshev polynomials of the third kind

“…The fractional order differential equations have been much studied and many aspects of these equations are explored. For some recent work on fractional diffusion equations, we can refer to different publications (see for instance, Loghmani (2013, 2014), Tadjeran (2004, 2006), Dehghan (2007, 2006), Sweilam and Khader (2010), Sweilam et al (2011Sweilam et al ( , 2012Sweilam et al ( , 2015) and the references therein.…”

Active Control of a Chaotic Fractional Order Economic System

“…Historical introductions on fractional-order differential equations (FDEs) can be found in [3][4][5][6]14]. Commonly-used definitions for fractional derivatives are due to Riemann-Liouville and Caputo [15].…”

“…However, applications of fractional calculus in physics and engineering have just begun. Many systems are known to display fractional order dynamics, such as viscoelastic systems, dielectric polarization and electromagnetic waves [1][2][3][4][5][6]. In recent years, the emergence of effective methods in differentiation and integration of non-integer order equations makes fractional order systems more and more attractive for the systems control community [7][8][9][10].…”

A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations

“…In addition, orthogonal polynomials have been widely used for obtaining numerical solutions for different types of FDEs. For example, Chebyshev polynomials of the second kind were employed by Sweilam et al for solving space fractional-order diffusion equations [10]. Moreover, Chebyshev polynomials of the first kind were used for solving some fractional differential equations in Khader and Sweilam [11].…”