The existence of the solution of a boundary value problem for Benjamin, Bona and Mahony type equation with the Hilfer fractional differential operator
The existence of the solution of a boundary value problem for Benjamin, Bona and Mahony type equation with the Hilfer fractional differential operator
Abstract
Annotation. In the present paper, we study the non-existence of the solution to the initialboundary value problem for time-fractional Benjamin, Bona and Mohany type equation in a rectangular
domain. To do this, we used the method proposed by Pokhojaev (see [1]) to analyze the perturbations of
solutions of nonlinear equations.
References
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T.B. Benjamin, J.L. Bona, J. J. Mahony. Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. Ser. A. 272, 47–78 (1972).
R.Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 200, p.87 and p.429.
R.Hilfer, Experimental evidence for fractional time evolution in glass materials, Chem. Physics 284(2002), 399-408.
