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Zbl 1189.65187
Zurigat, Mohammad; Momani, Shaher; Alawneh, Ahmad
Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method. (English)
[J] Comput. Math. Appl. 59, No. 3, 1227-1235 (2010). ISSN 0898-1221

Summary: We develop a framework to obtain approximate solutions to systems of algebraic-differential equations of fractional order by employing the homotopy analysis method (HAM). The study highlights the efficiency of the method and its dependence on the auxiliary parameter $\hbar$. Numerical examples are examined to highlight the significant features of the HAM method. The method shows improvements over existing analytical techniques

MSC 2000:: *65L99 Numerical methods for ODE
26A33 Fractional derivatives and integrals (real functions)
34A08
34A09 Implicit equations
34A45 Theoretical approximation of solutions of ODE

Keywords: systems of fractional algebraic-differential equations; homotopy analysis method; fractional differential equation

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Zentralblatt MATH Berlin [Germany]