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Invariant subspaces admitted by fractional differential equations with conformable derivatives

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  • Hashemi, M.S.

Abstract

There are various types of fractional derivatives in literature. One of the most natural and well-behaved fractional derivatives is recently introduced by the authors Khalil et al. [34], namely the conformable fractional derivative. In this paper, some more results about conformable fractional Laplace transform introduced by Abdeljawad [43] are investigated. The invariant subspace method is developed to get the exact solutions of various conformable time fractional differential equations. Finally, this theory is extended for the coupled system of conformable fractional differential equations, as well.

Suggested Citation

  • Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:161-169
    DOI: 10.1016/j.chaos.2018.01.002
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    4. Hassan Eltayeb & Said Mesloub & Yahya T. Abdalla & Adem Kılıçman, 2019. "A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations," Mathematics, MDPI, vol. 7(10), pages 1-21, October.
    5. Xu, Liguang & Hu, Hongxiao & He, Danhua, 2026. "Uniform boundedness and stability of fractional state-dependent delayed systems and applications to complex neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 599-615.
    6. Amjad E. Hamza & Mohamed Z. Mohamed & Eltaib M. Abd Elmohmoud & M. Magzoub, 2021. "Conformable Sumudu Transform of Space‐Time Fractional Telegraph Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    7. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    8. Ashpazzadeh, Elmira & Chu, Yu-Ming & Hashemi, Mir Sajjad & Moharrami, Mahsa & Inc, Mustafa, 2022. "Hermite multiwavelets representation for the sparse solution of nonlinear Abel’s integral equation," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    9. Martynyuk, Anatoliy A. & Stamov, Gani Tr. & Stamova, Ivanka M., 2020. "Fractional-like Hukuhara derivatives in the theory of set-valued differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    11. Alemayehu Tamirie Deresse, 2022. "Analytical Solution of One‐Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).

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