On Some Gamidov Integral Inequalities On Time Scales and Applications

Natural phenomena as well as problems encountered in pure and applied sciences are modeled by ordinary, partial or integral differential equations. Most of these problems have a nonlinear aspect which makes their studies difficult, or even impossible. For this, they must resort to other alternatives; among the methods used is the integral inequalities approach, which allows the study of quantitative and qualitative properties of solutions such as existence, uniqueness, delimitation, oscillation, and stability. In this study, we present some new integral inequalities of the Gronwall–Bellman–Bihari type associated with the fractional derivative of ψ-Hilfer, which represents a strong tool and is applicable in the study of certain differential equations. Several known results are derived and some applications to ordinary differential equations are provided to demonstrate the effectiveness of our finding.

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On Some Gamidov Integral Inequalities On Time Scales and Applications

Abstract: In the present paper, we extend Gamidov's integral inequalities to time scales. The obtained results can be used as tools in the study of certain properties of dynamical equations on time scales.

Cited by 3 publications

References 16 publications

Computational approach of dynamic integral inequalities with applications to timescale calculus

Computational approach of dynamic integral inequalities with applications to timescale calculus

A Note on Integral Inequalities on Time Scales Associated with Ostrowski’s Type

Some new Gronwall–Bellman–Bihari type integral inequality associated with ψ-Hilfer fractional derivative

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