Fractional Kdv and Boussenisq-burger's Equations, Reduction To Pde and Stability Approaches

Tantawy, M.Baleanu, D.Abdel-Gawad, H. I.2021-01-192025-09-182021-01-192025-09-182020Abdel-Gawad, H. I.; Tantawy, M.; Baleanu, Dumitru (2020). "Fractional KdV and Boussenisq-Burger's equations, reduction to PDE and stability approaches", Mathematical Methods in the Applied Sciences, Vol. 43, no. 7, pp. 4125-4135.0170-42141099-1476https://doi.org/10.1002/mma.6178https://hdl.handle.net/20.500.12416/11550Abdel-Gawad, Hamdy/0000-0003-1986-2324The generalized fractional Caputo-operator is discussed. The reduction of partial differential equations retarded or advanced with delays is obtained. The applications to the space-time-fractional KdV and time-fractional Boussenisq-Burger's equation are carried. Semi-self-similar SS wave solutions are obtained. That is, there exists a soliton wave propagates along a specific characteristic curve in the xt- plane. This may be due to the effects associated with the distributed time delay. The effects of space fractional derivative on a system are attributed to the transition states. Thus, anomalous wave transport is produced mainly near the origin.eninfo:eu-repo/semantics/closedAccessReduction To PdeGeneralized Time-Fractional OperatorSpace-Time Fractional KdvBoussenisq-Burger'S EquationsFractional Kdv and Boussenisq-burger's Equations, Reduction To Pde and Stability ApproachesFractional KdV and Boussenisq-Burger's equations, reduction to PDE and stability approachesArticle10.1002/mma.61782-s2.0-85078669704