TY - JOUR AU - El-Borai, Mahmoud M. AU - Awad, Hamed Kamal AU - Ali, Randa Hamdy M. PY - 2020 TI - On averaging methods for general parabolic partial differential equation JO - Journal of Mathematics and Computer Science SP - 164--175 VL - 21 IS - 2 AB - The averaging method of the quantitative and the qualitative analysis of the parabolic partial differential equations appears as an exciting field of the investigation. The aim of this paper is to generalize some known results due to Krol on the averaging methods and use them to solve the fractional parabolic partial differential equations and a special case of these equations is studied. We treat some different cases related to the averaging method. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.021.02.08 DO - 10.22436/jmcs.021.02.08 ID - El-Borai2020 ER - TY - JOUR TI - Method of averaging and the quantum anharmonic oscillator AU - A. Ben Lemlih AU - J. A. Ellison JO - Phys. Rev. Lett. PY - 1985 DA - 1985// VL - 55 ID - Lemlih1985 ER - TY - JOUR TI - On fundamental solutions of parabolic systems AU - S. D. Èĭdelʹman JO - Math. Sobornik PY - 1956 DA - 1956// VL - 38 ID - Èĭdelʹman1956 ER - TY - JOUR TI - Some probability densities and fundamental solutions of fractional evolution equations AU - M. M. El-Borai JO - Chaos Soliton Fractals PY - 2002 DA - 2002// VL - 14 ID - El-Borai2002 ER - TY - JOUR TI - Evolution equations without semi groups AU - M. M. El-Borai JO - J. Appl. Math. Comp. PY - 2004 DA - 2004// VL - 149 ID - El-Borai2004 ER - TY - JOUR TI - A parabolic transform and averaging methods for general partial differential equations AU - M. M. El-Borai AU - H. K. Awad AU - R. Hamdy AU - M. Ali JO - J. Adv. Math. PY - 2019 DA - 2019// VL - 17 ID - El-Borai2019 ER - TY - JOUR TI - A parabolic transform and some stochastic Ill-posed problem AU - M. M. El-Borai AU - K. El-Said El-Nadi JO - British J. Math. Comput. Sci. PY - 2015 DA - 2015// VL - 9 ID - El-Borai2015 ER - TY - JOUR TI - On the solutions of Ill-posed Cauchy problems for some singular integro-partial differential equations AU - M. M. El-Borai AU - K. El-Said El-Nadi JO - Global J. Math. PY - 2019 DA - 2019// VL - 13 ID - El-Borai2019 ER - TY - JOUR TI - On some fractional evolution equations AU - M. M. El-Borai AU - K. El-Said El-Nadi AU - E. G. El-Akabawy JO - Comput. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - El-Borai2010 ER - TY - JOUR TI - On some fractional stochastic delay differential equations AU - M. M. El-Borai AU - K. El-Said El-Nadi AU - H. A. Foad JO - Comput. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - El-Borai2010 ER - TY - JOUR TI - On the Cauchy problem for some parabolic fractional partial differential equations with time delays AU - M. M. El-Borai AU - W. G. El-Sayed AU - F. N. Ghaffoori JO - J. Math. Syst. Sci. PY - 2016 DA - 2016// VL - 6 ID - El-Borai2016 ER - TY - JOUR TI - On the correct formulation of a nonlinear differential equations in Banach space AU - M. M. El-Borai AU - O. L. Moustafa AU - F. H. Michael JO - Int. J. Math. Math. Sci. PY - 2001 DA - 2001// VL - 26 ID - El-Borai2001 ER - TY - BOOK TI - Partial Differential Equations of Parabolic Type AU - A. Friedman PB - Prentice-Hall PY - 1964 DA - 1964// CY - Englewood Cliffs ID - Friedman1964 ER - TY - JOUR TI - On the averaging method in nearly time-periodic advection-diffusion problems AU - M. S. Krol JO - SIAM J. Appl. Math. PY - 1991 DA - 1991// VL - 51 ID - Krol1991 ER - TY - BOOK TI - Maximum principles in differential equations AU - M. H. Protter AU - H. F. Weinberger PB - Prentice-Hall PY - 1967 DA - 1967// CY - Englewood Cliffs ID - Protter1967 ER - TY - JOUR TI - On averaging methods for partial differential equations AU - F. Verhulst JO - In: Symmetry and perturbation theory PY - 1999 DA - 1999// VL - 1999 ID - Verhulst1999 ER -