The Fractional Orthogonal Derivative

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Fractional Orthogonal Derivative

This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper by the author and Koornwinder in 2012. Here, an approximation of the Weyl or Riemann–Liouville fractional derivative is considered by replacing the n-th derivative...

متن کامل

Fractional Derivative as Fractional Power of Derivative

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

متن کامل

The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

متن کامل

Positive time fractional derivative

In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer order. The Fourier transform of the fractional time derivative in the Riemann-Liouville and Caputo senses, however, involves a complex power function of the fra...

متن کامل

Space-time Fractional Derivative Operators

Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics

سال: 2015

ISSN: 2227-7390

DOI: 10.3390/math3020273