| Keywords and phrases: fractional equation, non-boundary conditions, a priori estimates, pluriparabolic equation, non-classical function space, strong solution.
Received: November 6, 2021; Accepted: December 16, 2021; Published: January 8, 2022
How to cite this article: Moussa Zakari Djibibe, Bangan Soampa and Kokou Tcharie, Uniqueness of the solutions of nonlocal pluriparabolic fractional problems with weighted integral boundary conditions, Advances in Differential Equations and Control Processes 26 (2022), 103-112. DOI: 10.17654/0974324322007
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
References:
[1] B. Ahmad and J. Nieto, Existence results for nonlinear boundary value problems of fractional integro-differential equations with integral boundary conditions, Bound. Value Probl. 2009 (2009), 11, Article ID 708576.
[2] A. Anguraj and P. Karthikeyan, Existence of solutions for fractional semilinear evolution boundary value problem, Commun. Appl. Anal. 14 (2010), 505-514.
[3] M. Belmekki and M. Benchohra, Existence results for fractional order semilinear functional differential equations, Proc. A. Razmadze Math. Inst. 146 (2008), 9-20.
[4] M. Benchohra, J. R. Graef and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal. 87 (2008), 851-863.
[5] Moussa Zakari Djibibe, Bangan Soampa and Kokou Tcharie, A strong solution of a mixed problem with boundary integral conditions for a certain parabolic fractional equation using Fourier’s method, International Journal of Advances in Applied Mathematics and Mechanics 9(2) (2021), 1-6.
[6] Moussa Zakari Djibibe, Bangan Soampa and Kokou Tcharie, On solvability of an evolution mixed problem for a certain parabolic fractional equation with weighted integral boundary conditions in Sobolev function spaces, Universal Journal of Mathematics and Mathematical Sciences 14(2) (2021), 107-119.
[7] Djibibe Moussa Zakari and Ahcene Merad, On solvability of the third pseudo- parabolic fractional equation with purely nonlocal conditions, Advances in Differential Equations and Control Processes 23(1) (2020), 87-104.
[8] M. Z. Djibibe and K. Tcharie, On the solvability of an evolution problem with weighted integral boundary conditions in Sobolev function spaces with a priori estimate and Fourier’s method, British Journal of Mathematics and Computer Science 3(4) (2013), 801-810.
[9] N. J. Ford, J. Xiao and Y. Yan, A finite element method for time fractional partial differential equations, Frac. Calc. Appl. Anal. 14(3) (2011), 454-474. doi: 10.2478/s13540-011-0028-2.
[10] J. H. He, Nonlinear oscillation with fractional derivative and its applications, International Conference on Vibrating Engineering 98, Dalian, China, 1998, pp. 288-291.
[11] J. H. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol. 15 (1999), 86-90.
[12] 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, Communications in Computational Physics 8(5) (2010), 1016-1051.
[13] F. Dubois, A. C. Galucio and N. Point, Introduction à la dérivation fractionnaire: Théorie and Applications, 2010.
[14] V. E. Tarasov, Fractional integro-differential equations for electromagnetic waves in dielectric media, Theoret. and Math. Phys. 158(3) (2009), 355-359.
[15] Bangan Soampa and Moussa Zakari Djibibe, Mixed problem with an pure integral two-space-variables condition for a third order fractional parabolic equation, MJM 8(1) (2020), 258-271.
[16] Bangan Soampa, Moussa Zakari Djibibe and Kokou Tcharie, Analytical approximation solution of pseudo-parabolic fractional equation using a modified double Laplace decomposition method, Theoretical Mathematics and Applications 10(1) (2020), 17-31.
|
