Sentence examples for use the operational matrix from inspiring English sources

Another technique applied to solve FDE is to use the operational matrix of fractional order [2, 6, 11, 17].

Since one of our aims in this paper is to solve FDEs under different types of local and non-local boundary conditions, we have to face some complicated situations, so to handle these situations we will use the operational matrix developed in the next theorem.

One approach is based on converting differential equations into integral equations through integration, approximating various signals involved in the equation by truncated orthogonal series, and using the operational matrix of integration, to eliminate the integral operations [17].

By using the operational matrix of integration, we propose a new numerical method for linear fractional partial differential equation solving.

3, and we will solve two fractional-order equations using the operational matrix in Sect.

There are some papers in the literature about using the operational matrix of derivatives to solve differential equations [6, 18, 19].

In [21] Tripathi et al. presented an approximate solution of multi-term FDEs using the operational matrix of fractional integration of the generalized hat basis functions.

By using the operational matrix, the nonlinear fractional integro-differential equations are reduced to a system of algebraic equations which is solved through known numerical algorithms.

The introduced scheme here consists of expanding the fractional derivative of the state variable (D^{nu} x (t) ) with the Jacobi orthonormal polynomials with unknown coefficients using the operational matrix of fractional integrals.

In this section we solve nonlinear singular boundary value problem of the form Eq. (1) with the mixed conditions Eq. (2) and Eq. (3) by using the operational matrix of derivative [27] based on orthonormal Bernoulli polynomials.

Therefore, it is also interesting to consider spectral tau methods for solving multi-term FDEs on the half line by using the operational matrix of fractional integration of modified Laguerre polynomials.