Pseudospectral method for a one-dimensional fractional inverse problem.

In this paper, a method is implemented to a one-dimensional inverse problem with a parabolic differential equation of fractional order in which the fractional derivative is in the Caputo sense. The considered inverse problem involves a time-dependent source control parameter p (t). In order to numerically solve the problem, first, the main problem is converted to a homogeneous problem by Lagrange interpolation. Consequently, a new problem is derived by a practical technique that verifies all the conditions of the main problem. Finally, a system of nonlinear algebraic equations is solved by Newton's method to obtain the unknown coefficients. It is notable that all the needed computations are done in MATHEMATICA T M . In this work, operational matrices of Bernoulli polynomials are stated and applied to approximate functions. Illustrative examples are included to prove the efficiency and applicability of the proposed methods. In the numerical tests, a low amount of polynomials is needed to acquire a precise estimate solution. For demonstrating the low running time of this method, CPU time for all examples is exhibited. [ABSTRACT FROM AUTHOR]