English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The main attention of this work focus on extending the Lie symmetry and conservation law theories to the fractional partial differential equations involving the mixed derivative of the Riemann-Liouville time-fractional and first-order  x -derivatives. More specifically, we first present a new prolongation formula of the infinitesimal generators of Lie symmetries for the time-fractional breaking soliton equation since the equation involves the mixed derivative, then perform Lie symmetry analysis for the equation. Furthermore, we construct an optimal system of one-dimensional Lie subalgebras and use them to reduce the equation to lower-dimensional fractional partial differential equations involving the Erdélyi-Kober operator. In order to construct the power series solution of the equation, we introduce the Hadamard's finite-part integral to deal with the divergence of the integrals. The convergence and error estimate of the power series solution are proved. Finally, a new conservation law formula for the equation is given by means of the nonlinear self-adjointness method and nontrivial conservation laws are found.

Lie symmetry analysis, power series solutions and conservation laws of the time-fractional breaking soliton equation