New fractal–fractional parametric inequalities with applications

Saad Ihsan Butt and Ahmad Khan

Chaos, Solitons & Fractals, 2023, vol. 172, issue C

Abstract: In the present paper, we first establish a general parameterized identity for local fractional twice differentiable functions involving extended fractal–fractional integral operators. Thus by employing generalized convexity on differentiable mappings along with Yang’s Power-mean, Hölder’s and improved fractal integral inequalities lead us to develop variety of new fractal–fractional parameterized inequalities. Several examples are provided with graphical illustrations to prove the validity of new results. We give error analysis of improved bounds numerically and also by 2D, 3D graphical representations. Finally, we show that our main results recapture fractal variants of trapezoid, midpoint, Simpson and Bullen-type inequalities. Some related applications to the fractal means, moment of random variables and wave equations are given as well.

Keywords: Fractal theory; Generalized convex functions; Quadrature inequalities; Generalized fractional integral operators (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004307

DOI: 10.1016/j.chaos.2023.113529

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