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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].
(1) where M is called operational matrix of integration.
Recently, Singh et al. [36] derived the Bernstein operational matrix of integration.
Recently, Singh et al.[32] derived the Bernstein operational matrix of integration (see also[33]).
Note that, for (alpha=1), (F^{alpha}) is BPF's operational matrix of integration.
In Section 2, we introduce the Laguerre wavelets and the operational matrix of integration.
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Operational matrices of integration, delay and product are presented and are utilized to reduce the solution of multi-delay systems to the solution of algebraic equations.
We develop four operational matrices, two of them being operational matrices of integration and differentiation, the formulation technique for these two operational matrices is the same as that used for traditional orthogonal polynomials.
For the solution of such a problem Rehman and Khan [37, 38] introduced an efficient numerical scheme, based on the Haar wavelet operational matrices of integration for solving linear multi-point boundary value problems for FDEs.
Rehman and Khan [26] introduced a numerical scheme, based on the Haar wavelet operational matrices of integration for solving linear multi-point boundary value problems for fractional differential equations with constant and variable coefficients.
Heydari et al. [7] applied fractional operational matrix (FOM) of integration for the Legendre wavelets (LWs) to solve the problem.
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