Caputo fractional derivative operational matrices of Legendre and Chebyshev wavelets in fractional delay optimal control

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo used in quadratic optimization systems having fractional or integer orders differential equations. Using matrices, a new programming wavelet-based method without doing any integration operation for finding solutions optimal control traditional linear/nonlinear time-delay constrained/unconstrained is introduced. General strategies handling different types problems proposed.</p>