Extended Lie Method for Mixed Fractional Derivatives, Unconventional Invariants and Reduction, Conservation Laws and Acoustic Waves Propagated via Nonlinear Dispersive Equation

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann–Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications.

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Extended Lie Method for Mixed Fractional Derivatives, Unconventional Invariants and Reduction, Conservation Laws and Acoustic Waves Propagated via Nonlinear Dispersive Equation

Cited by 3 publications

References 47 publications

In plasma physics and fluid dynamics: Symbolic computation on a (2+1)-dimensional variable-coefficient Sawada-Kotera system

In plasma physics and fluid dynamics: Symbolic computation on a (2+1)-dimensional variable-coefficient Sawada-Kotera system

Invariant analysis, invariant subspace method and conservation laws of the (2+1)-dimensional mixed fractional Broer–Kaup–Kupershmidt system

Multidimensional Fractional Calculus: Theory and Applications

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