Sentence examples for matrix for fractional from inspiring English sources

The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann Liouville sense.

Podlubny proposed the matrix approach for fractional diffusion equations [22] and Hanert proposed a flexible numerical scheme for the discretization of the space-time fractional diffusion equation [23].

Podlubny et al. proposed the matrix approach for fractional diffusion equations [22], and Hanert proposed a flexible numerical scheme for the discretization of the space-time fractional diffusion equation [23].

The matrix approach for fractional diffusion equations was proposed in [25], and Hanert proposed a flexible numerical scheme for the discretization of the space-time fractional diffusion equation [26].

Let (D_{alpha}) is the block pulse operational matrix for the fractional differentiation.

Let (D^{alpha} ) be the block-pulse operational matrix for the fractional differentiation.

Now, the definition of CMGPS with complex transformation matrix is introduced for two fractional-order complex chaotic systems based on that of MGPS with real transformation matrix for two fractional-order real chaotic systems [13].

In order to use the tau method based on the operational matrix of fractional integration for modified generalized Laguerre for solving the fully integrated problem (22) with initial conditions (20), we approximate u ( x ) and g ( x ) by the modified generalized Laguerre polynomials as (23).

Next the definition of CMGPS with complex transformation matrix is introduced for the fractional-order complex chaotic drive system and the real chaotic response system based on that of MGPS with real transformation matrix for two fractional-order real chaotic systems [13].

Next the definition of CMGPS with complex transformation matrix is introduced for the fractional-order real chaotic drive system and the complex chaotic response system based on that of MGPS with real transformation matrix for two fractional-order real chaotic systems [13].

In the 'Application of Laguerre operational matrix for multi-order FDEs' subsection of the 'Methods' section, we apply the Laguerre operational matrix of fractional integration for solving linear multi-order FDEs.