This book, constancies the numerical solutions of fractional differential problems with initial (mixed boundary) conditions which have been considered in details. The fractional operational matrices of fractional derivative beta0 have been studied and developed on types of shifted chebyshev polynomials and shifted chebyshev wavelets as well as fractional order chebyshev polynomials with order 0 and presented the relation between these types, they are given as an operational matrices of fractional derivatives. Also the coupled fractional orders such that one of them is originally and others are axillary order such that one a fractional operational matrix to find the best approximate solution of multi-fractional order nonlinear differential problems with mixed boundary value. The rule of the order of fractional polynomial is presented as important parameter for given exact solution and is illustrated in some examples. ukryj opis