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The manuscript deals of the fractional optimal control problems (FOCPs) based on the Caputo fractional derivative by the ritz method. To use this method, we transform the FOCPs into an optimization problem and obtain the system of nonlinear algebraic equations. By polynomial basis functions, we approximate solutions. Then we have the coefficients of polynomial expansions by solving the system of nonlinear equations. numerical examples are presented which illustrate the performance of the method. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse source problem for a time-fractional equation with variable coefficients in a general bounded domain. The fractional derivative in the problem is in the Caputo sense. Transforming time-fractional inverse problems into optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation using Mathematica7 and we have the coefficients of polynomial expansion. We extensively discuss the convergence of the method. Illustrative examples are included to demonstrate the validity and applicability of the new technique. [ABSTRACT FROM AUTHOR]