A Parabolic Transform and Averaging Methods for General Partial Differential Equations

Mahmoud Mohammed Mostafa El-Borai; Hamed Kamal Awad Awad; Randa Hamdy. M. Ali Ali

doi:10.24297/jam.v17i0.8481

Authors

Mahmoud Mohammed Mostafa El-Borai Alexandria University
Hamed Kamal Awad Awad Damanhour University
Randa Hamdy. M. Ali Ali Damanhour University

DOI:

https://doi.org/10.24297/jam.v17i0.8481

Keywords:

Averaging Method, Parabolic Partial Differential Equation, Fractional Partial Di Erential Equation, Parabolic Transform, Existence And Uniqueness of Solutions

Abstract

Averaging method of the fractional general partial differential equations and a special case of these equations are studied, without any restrictions on the characteristic forms of the partial differential operators. We use the parabolic transform, existence and stability results can be obtained.

Downloads

Download data is not yet available.

Author Biographies

Mahmoud Mohammed Mostafa El-Borai, Alexandria University

Department of Mathematics, Faculty of Science, Alexandria University,
Alexandria, Egypt

Hamed Kamal Awad Awad, Damanhour University

Faculty of Science, Damanhour University, Behera, Egypt

Randa Hamdy. M. Ali Ali, Damanhour University

Faculty of Science, Damanhour University, Behera, Egypt

References

A. Ben Lemlih and J.A. Ellison, Method of averaging and the quantum anharmonic oscillator, Phys. Rev. Lett. 55 (1985), 1950-1953.

A. Friedman, Partial Di_erential Equations of Parabolic Type, Prentice-Hall, Englewood Cli_s, NJ (1964).

Krol, M.S., On the averaging method in nearly time-periodic advection-di_usion problems, SIAM J. Appl. Math. 51 (1991), 1622-1637.

Mahmoud M. El-Borai, Evolution equations without semi groups, J. of Appl. Math. And Comp., 149 (2004), 815-821.

Mahmoud M. El-Borai, Some probability densities and fundamental solutions of fractional evolution equations, Chaos, Soliton and Fractals 14 (2002), 433-440.

Mahmoud M. El-Borai, O. L. Moustafa, F. H. Michael, On the correct formulation of a nonlinear differential equations in Banach space, Int. J. Math. 22(1) (1999).

Mahmoud M. El-Borai, Khairia El-Said El-Nadi, A parabolic transform and some stochastic Ill-posed problem, British Journal of Mathematics and Computer Science, 9(5) (2015), 418-426.

Mahmoud M. El-Borai, Khairia El-Said El-Nadi, On the solutions of Ill-posed Cauchy problems for some singular integro-partial di_erential equations, Global Journal of Mathematics, 13(2) (2019), 899-905.

Mahmoud M. El-Borai, Khairia El-Said El-Nadi and Eman G. El-Akabawy, On some fractional evolution equations, Computers and Mathematics with Applications, 59 (2010), 1352-1355.

Mahmoud M. El-Borai, Khairia El-Said El-Nadi and Hoda A. Foad, On some fractional stochastic delay differential equations, Computers and Mathematics with Applications, 59 (2010), 1165-1170.

Mahmoud M. El-Borai, Wagdy G. El-Sayed, Faez N. Gha_oori, On the Cauchy problem for some parabolic fractional partial differential equations with time delays, Journal of Mathematics and System Science, 6 (2016), 194-199.

Protter, M.H., and Weinberger, H.F., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cli_s, NJ (1967).

Verhulst, F., On averaging methods for partial differential equations, SPT98-Symmetry and Perturbation Theory II, A.Degasperis and G.Gaeta eds., World Scientifc (1999), 79-95.