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Stability of solutions for generalized fractional differential problems by applying significant inequality estimates

Authors
  • Kassim, Mohammed D.1
  • Abdeljawad, Thabet2, 3, 4
  • Ali, Saeed M.1
  • Abdo, Mohammed S.5
  • 1 Imam Abdulrahman Bin Faisal University, Dammam, 34151, Saudi Arabia , Dammam (Saudi Arabia)
  • 2 Prince Sultan University, Riyadh, Saudi Arabia , Riyadh (Saudi Arabia)
  • 3 China Medical University, Taichung, 40402, Taiwan , Taichung (Taiwan)
  • 4 Asia University, Taichung, Taiwan , Taichung (Taiwan)
  • 5 Hodeidah University, Al-Hodeidah, Yemen , Al-Hodeidah (Yemen)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Aug 11, 2021
Volume
2021
Issue
1
Identifiers
DOI: 10.1186/s13662-021-03533-3
Source
Springer Nature
Keywords
Disciplines
  • Review
License
Green

Abstract

In this research paper, we intend to study the stability of solutions of some nonlinear initial value fractional differential problems. These equations are studied within the generalized fractional derivative of various orders. In order to study the solutions’ decay to zero as a power function, we establish sufficient conditions on the nonlinear terms. To this end, some versions of inequalities are combined and generalized via the so-called Bihari inequality. Moreover, we employ some properties of the generalized fractional derivative and appropriate regularization techniques. Finally, the paper involves examples to affirm the validity of the results.

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