In this manuscript, a new method is introduced for solving multi-order fractional differential equations. By transforming the fractional differential equations into an optimization problem and using polynomial basis functions, we obtain the system of algebraic equation. Then, we solve the system of nonlinear algebraic equation and obtain the coefficients of polynomial expansion. Also, we show the convergence of the method. Some numerical examples are presented which illustrate the theoretical results and the performance of the method.
On a Numerical Approach to Solve Multi-Order Fractional Differential Equations With Initial/Boundary Conditions
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 19, 2014; final manuscript received February 2, 2015; published online June 25, 2015. Assoc. Editor: J. A. Tenreiro Machado.
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Firoozjaee, M. A., Yousefi, S. A., Jafari, H., and Baleanu, D. (November 1, 2015). "On a Numerical Approach to Solve Multi-Order Fractional Differential Equations With Initial/Boundary Conditions." ASME. J. Comput. Nonlinear Dynam. November 2015; 10(6): 061025. https://doi.org/10.1115/1.4029785
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