Hadamard-Type Fractional Integro-Differential Problem: A Note on Some Asymptotic Behavior of Solutions

Ahmad Mugbil*, Nasser Eddine Tatar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


As a follow-up to the inherent nature of Hadamard-Type Fractional Integro-differential problem, little is known about some asymptotic behaviors of solutions. In this paper, an integro-differential problem involving Hadamard fractional derivatives is investigated. The leading derivative is of an order between one and two whereas the nonlinearities may contain fractional derivatives of an order between zero and one as well as some non-local terms. Under some reasonable condi-tions, we prove that solutions are asymptotic to logarithmic functions. Our approach is based on a generalized version of Bihari–LaSalle inequality, which we prove. In addition, several manipulations and crucial estimates have been used. An example supporting our findings is provided.

Original languageEnglish
Article number267
JournalFractal and Fractional
Issue number5
StatePublished - May 2022

Bibliographical note

Funding Information:
Funding: This research and the APC were funded by King Fahd University of Petroleum and Minerals through project number SB191023.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.


  • Hadamard fractional derivative
  • asymptotic behavior
  • fractional differential equation

ASJC Scopus subject areas

  • Analysis
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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