A new operational matrix for solving fractional-order differential equations

By Abbas Saadatmandi, Mehdi Dehghan. Computers and Mathematics with Applications, 2010

872 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/706a4c272eb2b4b440f8bc66645ddf60d95e413b

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In Control and Systems Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions (2014, methodology): “The authors of [28] presented a Legendre tau scheme combined with the operational matrix of Legendre polynomials for the numerical solution of multi-term FDEs.”
An Efficient Numerical Scheme for Solving Multi‐Dimensional Fractional Optimal Control Problems With a Quadratic Performance Index (2015, methodology): “The operational matrix of fractional derivatives was derived for some types of orthogonal polynomials such as, the Legendre [10], Chebyshev [11] and Jacobi [12] polynomials and used to solve several types of fractional differential equations, (see [13–15]).”
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, methodology): “There are some further methods, such as operational method [9], homotopy analysis method [10], differential transform method [11–13] and other methods [6,14–18].”
Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations (2013, methodology): “In [21], truncated Legendre series together with the Legendre operationalmatrix of fractional derivatives are used for the numerical integration of fractional differential equations.”
A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations (2015, background): “Operational matrices are used in several areas of numerical analysis and they hold particular importance for solving different kinds of problems in various subjects such as differential equations [47,48], integral equations [49], integro-differential equations [50,51], ordinary and partial fractiona”
New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations (2017, methodology): “In Figure 1, we compare the relative error obtained due to Genocchi polynomial operational matrix of fractional derivative (GPOMFD) and the Shifted Legendre operational matrix of fractional derivative (SLOMFD) derived in [17].”
A Legendre collocation method for fractional integro-differential equations (2011, methodology): “Legendre polynomials are a well-known family of orthogonal polynomials on the interval [ 1, 1] that have many applications (Saadatmandi and Dehghan, 2007, 2008, 2010a, b) They are widely used because of their good properties in the approximation of functions.”