Applications of Optimal Spline Approximations for the Solution of Nonlinear Time-Fractional Initial Value Problems

Nonlinear fractional differential equations are widely used to model real-life phenomena. For this reason, there is a need for efficient numerical methods solve such problems. In respect, collocation particularly attractive their ability deal with the nonlocal behavior of derivative. Among variety methods, based on spline approximations preferable since can be represented by local bases, thereby reducing computational load. paper, we use method quasi-interpolant operators nonlinear time-fractional initial value The tests performed show that has good approximation properties.