Abstract
In this manuscript we investigate the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE. The symmetry properties and reductions are derived. We construct the conservation laws (Cls) with Riemann–Liouville (RL) for the time fractional DLWE via a new conservation theorem. The conformable derivative is employed to establish soliton-like solutions for the governing equation by using the generalized projective method (GPM). Moreover, the Cls via the multiplier technique and the stability analysis via the concept of linear stability analysis for the integer order DLWE are established. Some graphical features are presented to explain the physical mechanism of the solutions.
Highlights
Fractional calculus has mesmerizing features due to its pragmatic applications in various areas of science, social science, finance, and engineering to mention a few
The conservation laws (Cls) have been utilized for developing numerical techniques, proving the existence and uniqueness of solutions [18], analysis of the internal characteristics like recursion operators, bi-Hamiltonian structures [19]
We investigate the Cls and soliton-like solutions of the time fractional DLWS with RL and conformable derivatives, respectively
Summary
Fractional calculus has mesmerizing features due to its pragmatic applications in various areas of science, social science, finance, and engineering to mention a few. A lot of meaningful definitions that have to do with fractional derivatives have been proposed by different authors in order to fully explain the memory effect [1,2,3,4]. The Cls have been utilized for developing numerical techniques, proving the existence and uniqueness of solutions [18], analysis of the internal characteristics like recursion operators, bi-Hamiltonian structures [19]. It should be noted that there have been numerous generalizations of Noether’s theorem and Euler–Lagrange’s [20] associating to several definitions of fractional derivative to establish Cls for fractional nonlinear PDEs possessing fractional Lagrangians [21,22,23]. We investigate the Cls and soliton-like solutions of the time fractional DLWS with RL and conformable derivatives, respectively. The αth extended infinitesimal related to the RL fractional time derivative with Eq (7) is given as in [38, 40, 41]
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