Abstract
(1) Background: symmetry breaking (self-organized transformation of symmetric stats) is a global phenomenon that arises in an extensive diversity of essentially symmetric physical structures. We investigate the symmetry breaking of time-2D space fractional wave equation in a complex domain; (2) Methods: a fractional differential operator is used together with a symmetric operator to define a new fractional symmetric operator. Then by applying the new operator, we formulate a generalized time-2D space fractional wave equation. We shall utilize the two concepts: subordination and majorization to present our results; (3) Results: we obtain different formulas of analytic solutions using the geometric analysis. The solution suggests univalent (1-1) in the open unit disk. Moreover, under certain conditions, it was starlike and dominated by a chaotic function type sine. In addition, the authors formulated a fractional time wave equation by using the Atangana–Baleanu fractional operators in terms of the Riemann–Liouville and Caputo derivatives.
Highlights
Symmetry breaking is a phenomenon in which small fluctuations performing on a system possessing a critical point adopts the system’s outcome, by defining which division of a bifurcation is occupied
Some results are discussed in the open unit disk
We propose a time-2D space fractional wave equation of a complex variable using the modified Atangana–Baleanu fractional differential operator without singular kernel, which is catting in a special class of normalized analytic functions in the open unit disk
Summary
Symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations performing on a system possessing a critical point (fixed point, the roots of the transform operator) adopts the system’s outcome, by defining which division of a bifurcation is occupied. This procedure is known symmetry breaking, because such changes typically transform the system from a symmetric but the disorganized state into one or more certain conditions. Sa et al [4] presented a review study on a complex-plane generalization of the successive distribution utilized to distinguish regular from chaotic quantum spectra.
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