Sentence examples for formula for fractional from inspiring English sources

Applications are also constructed by making use of some transformation formula for fractional derivatives.

First we state and prove an integration by parts formula for fractional sums.

Applications are constructed by making use of a transformation formula for fractional derivatives as well as generalized fractional derivatives.

Bhrawy et al. [16] proposed a new formula for fractional integrals of Chebyshev polynomials and application for solving multi-term fractional differential equations.

In Chen et al. [3], Hu et al. [4], Hu, Lu and Nualart [5],the authors discussed the Feynman-Kac formula for fractional heat equations.

These representations are found by making use of a new transformation formula for fractional derivatives published recently by the authors [16].

This technique requires a formula for fractional-order derivatives of shifted Legendre polynomials of any degree in terms of shifted Legendre polynomials themselves which is proved in Bhrawy et al. [19].

We end this paper by computing two special cases of Theorem 7. Note that calculations have been done with the help of standard formulas for fractional derivative operator acting on common functions (see [25, 26]).

In the first, we give a new formula for the fractional derivatives of the polynomials (phi_{i}(x)) in the sense of Riemann-Liouville, while the second gives the Riesz fractional derivatives for the same basis.

This approach is important to obtain the formula for the fractional difference derivative.

Recently, Tremblay et al. [16] discovered a new transformation formula for the fractional derivatives.