SOME NEW TYPES OF GRONWALL-BELLMAN INEQUALITY ON FRACTAL SET

Guotao Wang and Rong Liu
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Guotao Wang: School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030000, P. R. China
Rong Liu: School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030000, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-6

Abstract: Gronwall–Bellman-type inequalities provide a very effective way to investigate the qualitative and quantitative properties of solutions of nonlinear integral and differential equations. In recent years, local fractional calculus has attracted the attention of many researchers. In this paper, based on the basic knowledge of local fractional calculus and the method of proving inequality on the set of real numbers, some new Gronwall–Bellman inequalities are discussed and established on the fractal space. Our results are a powerful supplement to the existing literature.

Keywords: Fractal Space; Local Fractional Integral; Local Fractional Derivative; Gronwall–Bellman Inequality (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X2340114X

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