Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 127-138.

SOME NEW GRONWALL-BIHARI TYPE INEQUALITIES ASSOCIATED WITH GENERALIZED FRACTIONAL OPERATORS AND APPLICATIONS

Amira Ayari and Khaled Boukerrioua

Lanos Laboratory, University of Badji-Mokhtar, Annaba, Algeria
e-mail: ayari.amira1995@gmail.com
e-mail: khaledv2004@yahoo.fr

Abstract.   In this paper, we derive some generalizations of certain Gronwall-Bihari type inequality for generalized fractional operators unifying Riemann-Liouville and Hadamard fractional operators for functions in one variable, which provide explicit bounds on unknown functions.To show the feasibility of the obtained inequalities, two illustrative examples are also introduced.

2020 Mathematics Subject Classification.   26D15, 26A33, 26A42, 34A08, 34A12, 47B38.

Key words and phrases.   Gronwall-type inequality, Cauchy problem, mean value theorem, generalized fractional operators.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/ygjwrcpxdy

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