Nonlinear Functional Analysis and Applications

  • 제27권3호
  • /
  • Pages.679-689
  • /
  • 2022
  • /
  • 1229-1595(pISSN)
  • /
  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
권호 표지
DOI QR코드

DOI QR Code

A STUDY OF A WEAK SOLUTION OF A DIFFUSION PROBLEM FOR A TEMPORAL FRACTIONAL DIFFERENTIAL EQUATION

  • Anakira, Nidal (Department of Mathematics, Faculty of Science and Technology, Irbid National University) ;
  • Chebana, Zinouba (Department of Mathematics and Computer Science, University of Larbi Ben M'hidi) ;
  • Oussaeif, Taki-Eddine (Department of Mathematics and Computer Science, University of Larbi Ben M'hidi) ;
  • Batiha, Iqbal M. (Department of Mathematics, Faculty of Science and Technology, Irbid National University) ;
  • Ouannas, Adel (Department of Mathematics and Computer Science, University of Larbi Ben M'hidi)
  • 투고 : 2021.12.16
  • 심사 : 2022.03.15
  • 발행 : 2022.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we establish sufficient conditions for the existence and uniqueness of solution for a class of initial boundary value problems with Dirichlet condition in regard to a category of fractional-order partial differential equations. The results are established by a method based on the theorem of Lax Milligram.

키워드

참고문헌

  1. R.P. Agarwal, M. Benchohra and S. Hamani, Boundary value problems for fractional differential equations, Adv. Stud. Contemp. Math., 16 (2008), 181-196.
  2. G. Bahia, A. Ouannas, I.M. Batiha and Z. Odibat, The optimal homotopy analysis method applied on nonlinear time-fractional hyperbolic partial differential equations, Numer. Methods Part. Diff. Equ., 37(3) (2021), 2008-2022. https://doi.org/10.1002/num.22639
  3. K. Balachandran, L. Byszewski and J.K. Kim, Nonlocal Cauchy problem for second order functional differential equations and fractional differential equations, Nonlinear Funct. Anal. Appl., 24(3) (2019), 457-475.
  4. N. Djenina, A. Ouannas, I.M. Batiha, G. Grassi and V-T. Pham, On the stability of linear incommensurate fractional-order difference systems, Mathematics, 8(10) (2020), 1754. https://doi.org/10.3390/math8101754
  5. J.H. He, Nonlinear oscillation with fractional derivative and its applications, International Conference on Vibrating Engineering'98, Dalian, China, (1998), 288-291.
  6. J.H. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol., 15 (1999), 86-90.
  7. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng., 167 (1998), 57-68. https://doi.org/10.1016/S0045-7825(98)00108-X
  8. A-A. Khennaoui, A. Ouannas, S. Momani, I.M. Batiha, Z. Dibi and G. Grassi, On dynamics of a fractional-order discrete system with only one nonlinear term and without fixed points, Electronics, 9(12) (2020), 2179. https://doi.org/10.3390/electronics9122179
  9. B. Khaminsou, Ch. Thaiprayoon, W. Sudsutad and S.A. Jose, Qualitative analysis of a proportional Caputo fractional Pantograph differential equation with mixed nonlocal conditions, Nonlinear Funct. Anal. Appl., 26(1) (2021), 197-223.
  10. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  11. X.J. Li and C.J. Xu, Existence and uniqueness of the weak solution of the space-time fractional diffusion equation and a spectral method approximation, Commu. Comput. Phys., 8(5) (2010), 1016-1051. https://doi.org/10.4208/cicp.020709.221209a
  12. X.J. Li and C.J. Xu, A space-time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal., 47(3) (2009), 2108-2131. https://doi.org/10.1137/080718942
  13. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, J. Wiley, New York, 1993.
  14. A. Ouannas, F. Mesdoui, S. Momani, I. Batiha and G. Grassi, Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law, Archives of Control Sci., 31(2) (2021), 333-345.
  15. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
  16. I. Talbi, A. Ouannas, A-A. Khennaoui, A. Berkane, I.M. Batiha, G. Grassi and V-T. Pham, Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization, Adv. Differ. Equ., 2020 (2020), 624. https://doi.org/10.1186/s13662-020-03086-x