Fractional order integrodifferential equations cannot be directly solved like ordinary differential equations. Numerical methods for such equations have additional algorithmic complexities. We present a particularly simple recipe for solving such equations using a Galerkin scheme developed in prior work. In particular, matrices needed for that method have here been precisely evaluated in closed form using special functions, and a small Matlab program is provided for the same. For equations where the highest order of the derivative is fractional, differential algebraic equations arise; however, it is demonstrated that there is a simple regularization scheme that works for these systems, such that accurate solutions can be easily obtained using standard solvers for stiff differential equations. Finally, the role of nonzero initial conditions is discussed in the context of the present approximation method.
Simple Recipe for Accurate Solution of Fractional Order Equations
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received May 4, 2012; final manuscript received October 21, 2012; published online December 19, 2012. Assoc. Editor: J. A. Tenreiro Machado.
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Das, S., and Chatterjee, A. (December 19, 2012). "Simple Recipe for Accurate Solution of Fractional Order Equations." ASME. J. Comput. Nonlinear Dynam. July 2013; 8(3): 031007. https://doi.org/10.1115/1.4023009
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