| Keywords and phrases: fractional equation, non boundary conditions, functional analysis method, non-classical function space, strong solution, energy inequality.
Received: December 3, 2021; Accepted: January 24, 2022; Published: January 29, 2022
How to cite this article: AMETANA Edoh, DJIBIBE Moussa Zakari and ALEDA Koulinté, Strongly generalized solution of a fractional problem of parabolic evolution of order-two in a plate with integral boundary conditions, Advances in Differential Equations and Control Processes 26 (2022), 131-141. DOI: 10.17654/0974324322009
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References:
[1] B. Ahmad and J. Nieto, Existence results for nonlinear boundary value problems of fractional integro-differential equations with integral boundary conditions, Boundary Value Problems 2009 (2009), 11 pages, 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), 920.
[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] Djibibe Moussa Zakari, Soampa Bangan and Tcharie Kokou, 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.
[6] Djibibe Moussa Zakari, Soampa Bangan and Tcharie Kokou, 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.
[7] Djibibe Moussa Zakari, Soampa Bangan and Tcharie Kokou, 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 12(2) (2021), 107-119.
[8] 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.
[9] Djibibe Moussa Zakari and Tcharie Kokou, 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 Mathematic and Computer Science 3(4) (2013), 801-810.
[10] N. J. Ford, J. Xiao and Y. Yan, A finite element method for time fractional partial differential equations, Fractional Calculus and Applied Analysis 14(3) (2011), 454-474. doi: 10.2478/s13540-011-0028-2
[11] J. H. He, Nonlinear oscillation with fractional derivative and its applications, International Conference on Vibrating Engineering 98, Dalian, China, 1998, pp. 288-291.
[12] J. H. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol. 15 (1999), 86-90.
[13] 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.
[14] Soampa Bangan and Djibibe Moussa Zakari, Mixed problem with a pure integral two-space-variables condition for a third order fractional parabolic equation, Malaya Journal of Matematik 8(1) (2020), 258-271.
[15] Soampa Bangan, Djibibe Moussa Zakari 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.
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