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PreprintCC BY-NC-SA 4.0HAL

Asymptotic behavior of bounded Mild Solutions to some fractional differential equations involving the ψ-Hilfer derivative

  • Adama Kabore
  • Pihiré Vincent Ouena
  • Moumini Kéré
  • Gaston Mandata N'Guérékata
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Abstract

In this paper, we investigate further properties of bounded continuous functions that behave like almost automorphic functions at infinity. We then apply the results to study the existence and uniqueness of mild solutions to some fractional differential equations involving the ψ-Hilfer derivative in Banach spaces. We use some new properties of the two-parameter Mittag-Leffler function the Banach's fixed point principle to achieve our results. This work is new in the context of evolution equations governed by the ψ-Hilfer derivative.

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Cite

BibTeXRIS
BibTeX
@misc{kabore2026asymptotic,
  title = {{Asymptotic behavior of bounded Mild Solutions to some fractional differential equations involving the $\psi$-Hilfer derivative}},
  author = {Adama Kabore and Pihiré Vincent Ouena and Moumini Kéré and Gaston Mandata N'Guérékata},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05762642v1},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Asymptotic behavior of bounded Mild Solutions to some fractional differential equations involving the ψ-Hilfer derivative
AU  - Adama Kabore
AU  - Pihiré Vincent Ouena
AU  - Moumini Kéré
AU  - Gaston Mandata N'Guérékata
PY  - 2026
DA  - 2026/09/24
PB  - HAL
UR  - https://hal.science/hal-05762642v1
AB  - In this paper, we investigate further properties of bounded continuous functions that behave like almost automorphic functions at infinity. We then apply the results to study the existence and uniqueness of mild solutions to some fractional differential equations involving the ψ-Hilfer derivative in Banach spaces. We use some new properties of the two-parameter Mittag-Leffler function the Banach's fixed point principle to achieve our results. This work is new in the context of evolution equations governed by the ψ-Hilfer derivative.
ER  -