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Solvability of pseudoparabolic equation with Caputo fractional derivative

Author

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  • Aitzhanov, S.E.
  • Kusherbayeva, U.R.
  • Bekenayeva, K.S.

Abstract

This paper is devoted to the study of solvability of the problem for a pseudo-parabolic equation with a Caputo fractional derivative. The existence of the weak solution is investigated by applying Galerkin approximations and a priori estimates. On the way to prove the weak solution's uniqueness of the problem the Sobolev embedding theorem, Rellich-Kondrashov theorem and Gronwall-Bellman Lemma are applied. Along with this, the blow up of the solution to the problem in finite time is proved. The global solvability of the initial boundary value problem and the uniqueness of the weak generalized solution have been studied.

Suggested Citation

  • Aitzhanov, S.E. & Kusherbayeva, U.R. & Bekenayeva, K.S., 2022. "Solvability of pseudoparabolic equation with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004039
    DOI: 10.1016/j.chaos.2022.112193
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    References listed on IDEAS

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    1. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
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