Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order. (English) Zbl 1116.35046

Summary: We propose an extension of the Lagrange method of characteristics for solving a class of nonlinear partial differential equations of fractional order. This refers to the Lagrange method of the auxiliary system for linear fractional partial differential equations (which is given in an appendix). The key to the approach is the Taylor’s series of fractional order \(f(x+h) = E_{\alpha}(h^{\alpha}D^{\alpha}_{x})f(x)\), where \(E_{\alpha }\) is the Mittag-Leffler function.


35G20 Nonlinear higher-order PDEs
26A33 Fractional derivatives and integrals
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