New fractal–fractional parametric inequalities with applications

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 improv...

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Bibliographic Details
Published in:Chaos, solitons and fractals Vol. 172; p. 113529
Main Authors: Butt, Saad Ihsan, Khan, Ahmad
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.07.2023
Subjects:
Fractal theory
Generalized convex functions
Generalized fractional integral operators
Quadrature inequalities
Quadrature inequalities
Fractal theory
Generalized convex functions
Generalized fractional integral operators
ISSN:0960-0779
Online Access:Get full text
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Summary: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. •Contain interesting results linking fractal–fractional analysis on fractal sets and inequality theory.•New Fractal Parameterized inequalities are introduced by utilizing extended fractional integral operators.•New approaches are used to obtain improve bounds.•Error analysis on bounds and its graphical analysis is provided to show the validity of obtain results.•Some related applications to the fractal means, moment of random variables and wave equations are given as well.
ISSN:0960-0779
DOI:10.1016/j.chaos.2023.113529