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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| Vydané v: | Chaos, solitons and fractals Ročník 172; s. 113529 |
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| Jazyk: | English |
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Elsevier Ltd
01.07.2023
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| ISSN: | 0960-0779 |
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| 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.
•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. |
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| AbstractList | 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. |
| ArticleNumber | 113529 |
| Author | Khan, Ahmad Butt, Saad Ihsan |
| Author_xml | – sequence: 1 givenname: Saad Ihsan orcidid: 0000-0001-7192-8269 surname: Butt fullname: Butt, Saad Ihsan email: saadihsanbutt@gmail.com – sequence: 2 givenname: Ahmad surname: Khan fullname: Khan, Ahmad email: itsahmadkhaan@gmail.com |
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| Cites_doi | 10.1002/mma.7081 10.1142/S0218348X21501267 10.1016/j.mcm.2011.05.026 10.1142/S0218348X22500852 10.1016/j.chaos.2019.109547 10.1016/j.cam.2014.01.002 10.1002/mma.5975 10.1142/S0218348X21500985 10.1016/j.aej.2020.10.038 10.1016/j.chaos.2020.110554 10.2989/16073606.2018.1509242 10.1016/j.chaos.2022.112602 10.1002/mma.6319 10.1002/mma.3808 10.1142/S0218348X22400084 10.1142/S0218348X22400552 10.1016/j.cam.2020.112740 10.1016/j.chaos.2021.111025 10.1016/j.chaos.2022.112661 10.18514/MMN.2018.2441 10.3390/sym13122249 10.1016/S0034-4877(17)30059-9 10.2298/FIL2312737B 10.1016/j.aej.2021.10.033 10.1142/S0218348X21500067 |
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| SubjectTerms | Fractal theory Generalized convex functions Generalized fractional integral operators Quadrature inequalities |
| Title | New fractal–fractional parametric inequalities with applications |
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