SavedAdd your journal

Journals / Cankaya University Journal of Science and Engineering / 2026 / Volume: 20 Issue: 1

Convergent Result for Linear Conformable Pseudo-parabolic Equation

Tuan Nguyen Anh0000-0002-8757-9742
Ngo Hung0000-0002-4380-0257
Hoang Luc Nguyen0000-0001-9664-6743
Pages
—
Publication Date
2023-05-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The main technique is to use evaluations in Hilbert scales spaces that incorporate some new inequalities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we are interested to study conformable pseudo-parabolic equation.
📊
Key Findings & Data:Our main goal is to show that the convergence result of the mild solution when the fractional order tends to 1−.
💡
Conclusion & Impact:The main technique is to use evaluations in Hilbert scales spaces that incorporate some new inequalities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional derivative · Pseudo-parabolic equation · Well–posedness

Abstract

In this paper, we are interested to study conformable pseudo-parabolic equation. This equation has many applications in science and engineering. Our main goal is to show that the convergence result of the mild solution when the fractional order tends to 1−. The main technique is to use evaluations in Hilbert scales spaces that incorporate some new inequalities.

🔖

Cite This Article

Anh, T. N., Hung, N., Nguyen, H. L. (2023). Convergent Result for Linear Conformable Pseudo-parabolic Equation. Cankaya University Journal of Science and Engineering, Volume: 20 Issue: 1. https://ajindex.com/articles/1468645

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (19)

  1. V. Kiryakova, ”Generalized Fractional Calculus and Applications,” Pitman Research Notes in Mathematics 301, Longman, Harlow 1994.
  2. I. Podlubny, ”Fractional Differential Equations,” Academic Press, California, 1999.
  3. V.F. Morales-Delgado, J.F. Go´mez-Aguilar, R.F. Escobar-Jime´nez and M.A. Taneco-Herna´ndez, ”Fractional conformable derivatives of Liouville-Caputo type with low-fractionality,” Physica A: Statistical Mechanics and its Applications, vol. 503, pp. 424-438, 2018.
  4. S. He, K. Sun, X. Mei, B. Yan and S. Xu, ”Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative,” Eur. Phys. J. Plus, vol. 132, no. 36, 2017.
  5. N.H. Tuan, T.B. Ngoc, D. Baleanu and D. O’Regan, ”On well-posedness of the sub-diffusion equation with conformable derivative model,” Communications in Nonlinear Science and Numerical Simulation, vol. 89, pp. 26, 2020.
  6. N.N. Hung, H.D. Binh and N.H. Luc, ”Stochastic sub-diffusion equation with conformable derivative driven by standard Brownian motion,” Advances in Theory of Nonlinear Analysis and its Applications, vol. 5, no. 3, pp. 287–299, 2021.
  7. T.Q. Minh and V.T. Thi, ”Some sharp results about the global existence and blowup of solutions to a class of coupled pseudo-parabolic equations,” J. Math. Anal. Appl.” vol. 506, no. 2, pp. 39, 2022.
  8. N.H. Tuan, V.V.Au and R. Xu, ”Semilinear Caputo time-fractional pseudo-parabolic equations,” Commun. Pure Appl. Anal., vol. 20, no. 2, pp. 583–621, 2021.
  9. X. Wang and R. Xu, ”Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation,” Adv. Nonlinear Anal., vol. 10, no. 1, pp. 261-288, 2021.
  10. R. Xu, X. Wang and Y. Yang, ”Blowup and blowup time for a class of semilinear pseudo-parabolic equations with high initial energy,” Appl. Math. Lett., vol. 83, pp. 176-181, 2018.
  11. R. Xu and J. Su, ”Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equa- tions,” Journal of Functional Analysis, vol. 264, no. 12, pp. 2732-2763, 2013.
  12. N.H. Luc, J. Hossein, P. Kumam and N.H. Tuan, ”On an initial value problem for time fractional pseudo- parabolic equation with Caputo derivative,” Math. Methods Appl. Sci., https://doi.org/10.1002/mma.7204.
  13. R. Shen, M. Xiang and V. D. Ra˘dulescu, ”Time-Space Fractional Diffusion Problems: Existence, Decay Estimates and Blow-Up of Solutions,” Milan Journal of Mathematics, 2022.
  14. N.A. Tuan, Z. Hammouch, E. Karapinar and N.H. Tuan, ”On a nonlocal problem for a Caputo time-fractional pseudoparabolic equation,” Math. Methods Appl. Sci., vol. 44, no. 18, pp. 14791-14806, 2021.
  15. N.H. Tuan, N.V. Tien and C. Yang, ”On an initial boundary value problem for fractional pseudo-parabolic equation with conformable derivative,” vol. 19, no. 11, pp. 11232-11259, 2022.
  16. T. Abdeljawad, ”On conformable fractional calculus,” J. Comput. Appl. Math., vol. 279, pp. 57-66, 2015. [17] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, ”A new definition of fractional derivative,” J. Comput. Appl. Math., vol. 264, pp. 65–70, 2014.
  17. A. Jaiswal and D. Bahuguna, ”Semilinear Conformable Fractional Differential Equations in Banach Spaces,” Differ. Equ. Dyn. Syst., vol. 27, no. 1-3, pp. 313-325, 2019.
  18. A.A. Abdelhakim, J.A. and Tenreiro Machado, ”A critical analysis of the conformable derivative,” Nonlinear Dynamics, vol. 95, no. 4, pp 3063-3073, 2019.
  19. N.H. Tuan, N.V. Tien, D. O’regan, N.H. Can and V.T. Nguyen, ”New results on continuity by order of deriva- tive for conformable parabolic equations,” Fractals, to appear, https://doi.org/10.1142/S0218348X23400145.