Khoshsiar Ghaziani, R., Fardi, M., Ghasemi, M. (2016). Solving multi-order fractional differential equations by reproducing kernel Hilbert space method. Computational Methods for Differential Equations, 4(3), 170-190.
Reza Khoshsiar Ghaziani; Mojtaba Fardi; Mehdi Ghasemi. "Solving multi-order fractional differential equations by reproducing kernel Hilbert space method". Computational Methods for Differential Equations, 4, 3, 2016, 170-190.
Khoshsiar Ghaziani, R., Fardi, M., Ghasemi, M. (2016). 'Solving multi-order fractional differential equations by reproducing kernel Hilbert space method', Computational Methods for Differential Equations, 4(3), pp. 170-190.
Khoshsiar Ghaziani, R., Fardi, M., Ghasemi, M. Solving multi-order fractional differential equations by reproducing kernel Hilbert space method. Computational Methods for Differential Equations, 2016; 4(3): 170-190.
Solving multi-order fractional differential equations by reproducing kernel Hilbert space method
Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran
Abstract
In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error analysis for the proposed technique in different reproducing kernel Hilbert spaces and present some useful results. The accuracy of the proposed technique is examined by comparing with the exact solution of some test examples.
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