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A NEW FORMULA FOR ADOMIAN POLYNOMIALS AND THE ANALYSIS OF ITS TRUNCATED SERIES SOLUTION FOR FRACTIONAL NON-DIFFERENTIABLE INITIAL VALUE PROBLEMS

Part of: Real functions Equations and systems with constant coefficients Error analysis and interval analysis

Published online by Cambridge University Press:  20 November 2013

M. M. KHADER
M. M. KHADER*
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
*
mohamedmbd@yahoo.com
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Abstract

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A new formula for Adomian polynomials is introduced and applied to obtain truncated series solutions for fractional initial value problems with nondifferentiable functions. These kinds of equations contain a fractional single term which is examined using Jumarie fractional derivatives and fractional Taylor series for nondifferentiable functions. The property of nonlocality of these equations is examined, and the existence and uniqueness of solutions are discussed. Convergence and error analysis for the Adomian series solution are also studied. Numerical examples show the accuracy and efficiency of this formula for solving initial value problems for high-order fractional differential equations.

Keywords

Adomian polynomialsJumarie fractional derivativesnondifferentiable initial value problemsnonlocality propertyerror and convergence analysis

MSC classification

Secondary: 65K10: Optimization and variational techniques 65G99: None of the above, but in this section 26A33: Fractional derivatives and integrals 35E99: None of the above, but in this section 68U20: Simulation
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 1 , July 2013 , pp. 69 - 92
Copyright
Copyright ©2013 Australian Mathematical Society 

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