# 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

S.I. Pokhozhaev, Essentially nonlinear capacities induced by differential operators, Dokl.Ros. Akad. Nauk. 357(5) (1997), 592-594.

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.

## Published

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/594