GLOBAL EXISTENCE AND CONTINUOUS DEPENDENCE ON PARAMETERS OF CONFORMABLE PSEUDO-PARABOLIC INCLUSION

Le Dinh Long; Vo Ngoc Minh; Yusuf Gurefe; Yusuf Pandir

doi:10.11948/20230246

2024 Volume 14 Issue 2

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Le Dinh Long, Vo Ngoc Minh, Yusuf Gurefe, Yusuf Pandir. GLOBAL EXISTENCE AND CONTINUOUS DEPENDENCE ON PARAMETERS OF CONFORMABLE PSEUDO-PARABOLIC INCLUSION[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 986-1005. doi: 10.11948/20230246

Citation:

Le Dinh Long, Vo Ngoc Minh, Yusuf Gurefe, Yusuf Pandir. GLOBAL EXISTENCE AND CONTINUOUS DEPENDENCE ON PARAMETERS OF CONFORMABLE PSEUDO-PARABOLIC INCLUSION[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 986-1005. doi: 10.11948/20230246

GLOBAL EXISTENCE AND CONTINUOUS DEPENDENCE ON PARAMETERS OF CONFORMABLE PSEUDO-PARABOLIC INCLUSION

1.
Faculty of Maths, FPT University HCM, Saigon Hi-tech Park, Ho Chi Minh City, Vietnam
2.
Faculty of Mathematics and Computer Science, University of Science, 227 Nguyen Van Cu St., Dist. 5, Ho Chi Minh City, Vietnam
3.
Vietnam National University, Ho Chi Minh City, Vietnam
4.
Department of Mathematics, Faculty of Science, Mersin University, Mersin, Turkey
5.
Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, Yozgat, Turkey

Author Bio: Email: ledinhlong@vlu.edu.vn(L. D. Long); Email: pinkpantherminh@gmail.com(V. N. Minh); Email: ygurefe@gmail.com(Y. Gurefe)
Corresponding author: Email: yusufpandir@gmail.com(Y. Pandir)

Abstract

Abstract

In this paper, we establish global existence and continuous dependence on parameters for sets of solutions of the differential inclusion including self-adjoint operators with fractional order in the form
$\left\{\begin{array}{lr}\frac{{ }^C \partial^\alpha}{\partial t^\alpha} u(t)+m \mathcal{L}^{s_1} \frac{{ }^C \partial^\alpha}{\partial t^\alpha} u(t)+\mathcal{L}^{s_2} u(t) \in F(t, u(t), \eta), & t \in[0, T), \\u(0)=\varphi, & \text { on } \mathcal{D},\end{array}\right.$
where $ s_1, s_2>0 $. We first use spectral theory on Hilbert spaces to obtain formulation for mild solutions. With this formulation, we use a measure of noncompactness with values in ordered space to construct useful bounds for solution operators. Then, we establish necessarily upper semicontinuous and condensing settings, which mainly help to obtain the global existence of mild solutions and the compactness of the mild solutions set. Before ending the article, we discuss the continuous dependence of the solution set when the input data contains the parameter $ \eta $.
- Multi-function /
- measure of compactness /
- differential inclusion /
- self-adjoint operator
MSC: 35R11, 35B65, 26A33

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References

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