A fractional spectral method with applications to some singular problems
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Computational Mathematics"
DOI: 10.1007/s10444-016-9511-y
Abstract: In this paper we propose and analyze fractional spectral methods for a class of integro-differential equations and fractional differential equations. The proposed methods make new use of the classical fractional polynomials, also known as Müntz… read more here.
Keywords: applications singular; integro differential; spectral method; differential equations ... See more keywords
A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels
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DOI: 10.1007/s10915-019-00987-2
Abstract: The classical integer-order Jacobi spectral methods for solving second kind nonlinear Volterra integral equations with weakly singular kernels may cause a low-order accuracy in numerically approximating the exact solution. To overcome the shortcomings, we in… read more here.
Keywords: collocation; integral equations; volterra integral; fractional spectral ... See more keywords
Fractional Spectral Analysis of Randomly Sampled Signals and Applications
Sign Up to like & getrecommendations! Published in 2017 at "IEEE Transactions on Instrumentation and Measurement"
DOI: 10.1109/tim.2017.2728438
Abstract: Nonuniform sampling can be utilized to achieve certain desirable results. Periodic nonuniform sampling can decrease the required sampling rate for signals. Random sampling can be used as a digital alias-free signal processing method in analog-to-digital… read more here.
Keywords: estimation; fractional spectral; random sampling; spectral analysis ... See more keywords
Exact Closed-Form Fractional Spectral Moments for Linear Fractional Oscillators Excited by a White Noise
Sign Up to like & getrecommendations! Published in 2017 at "ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering"
DOI: 10.1115/1.4036700
Abstract: In the last decades the research community has shown an increasing interest in the engineering applications of fractional calculus, which allows to accurately characterize the static and dynamic behaviour of many complex mechanical systems, e.g.… read more here.
Keywords: moments linear; linear fractional; closed form; spectral moments ... See more keywords
Fractional spectral differentiation matrices based on Legendre approximation
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Difference Equations"
DOI: 10.1186/s13662-020-02590-4
Abstract: A simple scheme is proposed for computing N × N $N \times N$ spectral differentiation matrices of fractional order α for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous… read more here.
Keywords: legendre approximation; fractional spectral; differentiation matrices; spectral differentiation ... See more keywords