New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity
This paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal–fractional inequalities, presenting a range of results not only f...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/25 |
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| author | Wedad Saleh Hamid Boulares Abdelkader Moumen Hussien Albala Badreddine Meftah |
| author_facet | Wedad Saleh Hamid Boulares Abdelkader Moumen Hussien Albala Badreddine Meftah |
| author_sort | Wedad Saleh |
| collection | DOAJ |
| description | This paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal–fractional inequalities, presenting a range of results not only for fractional integrals and fractal calculus, but also offering a refinement of the well-known Bullen-type inequality. We further explore the connections between generalized convexity and fractal–fractional integrals, showing how the concept of generalized convexity enables the establishment of error bounds for fractal–fractional integrals involving lower-order derivatives, with an emphasis on their applications in various fields. The findings expand the current understanding of fractal–fractional inequalities and offer new insights into the use of local fractional derivatives for analyzing functions with fractional-order properties. |
| format | Article |
| id | doaj-art-fd3a8319f09440418a45634046823d1a |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-fd3a8319f09440418a45634046823d1a2025-01-24T13:33:24ZengMDPI AGFractal and Fractional2504-31102025-01-01912510.3390/fractalfract9010025New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized ConvexityWedad Saleh0Hamid Boulares1Abdelkader Moumen2Hussien Albala3Badreddine Meftah4Department of Mathematics, Taibah University, Al Medinah 42353, Saudi ArabiaLaboratory of Analysis and Control of Differential Equations “ACED”, Facuty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, AlgeriaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaTechnical and Engineering Unit, Applied College (Tanomah), King Khalid University, Abha 61413, Saudi ArabiaLaboratory of Analysis and Control of Differential Equations “ACED”, Facuty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, AlgeriaThis paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal–fractional inequalities, presenting a range of results not only for fractional integrals and fractal calculus, but also offering a refinement of the well-known Bullen-type inequality. We further explore the connections between generalized convexity and fractal–fractional integrals, showing how the concept of generalized convexity enables the establishment of error bounds for fractal–fractional integrals involving lower-order derivatives, with an emphasis on their applications in various fields. The findings expand the current understanding of fractal–fractional inequalities and offer new insights into the use of local fractional derivatives for analyzing functions with fractional-order properties.https://www.mdpi.com/2504-3110/9/1/25Bullen inequalityfractal–fractional integralsgeneralized convexityfractal sets |
| spellingShingle | Wedad Saleh Hamid Boulares Abdelkader Moumen Hussien Albala Badreddine Meftah New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity Fractal and Fractional Bullen inequality fractal–fractional integrals generalized convexity fractal sets |
| title | New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity |
| title_full | New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity |
| title_fullStr | New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity |
| title_full_unstemmed | New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity |
| title_short | New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity |
| title_sort | new approaches to fractal fractional bullen s inequalities through generalized convexity |
| topic | Bullen inequality fractal–fractional integrals generalized convexity fractal sets |
| url | https://www.mdpi.com/2504-3110/9/1/25 |
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