On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application
Abstract Post-quantum integral inequalities involving the Riemann–Liouville fractional integral have a significant role in understanding and modeling systems with nonlocal interactions; anomalous diffusion and memory effects make them indispensable for addressing modern challenges in applied mathema...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03345-z |
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| author | Sobia Rafeeq Sabir Hussain Drakhshan Mansab Hijaz Ahmad Taha Radwan |
| author_facet | Sobia Rafeeq Sabir Hussain Drakhshan Mansab Hijaz Ahmad Taha Radwan |
| author_sort | Sobia Rafeeq |
| collection | DOAJ |
| description | Abstract Post-quantum integral inequalities involving the Riemann–Liouville fractional integral have a significant role in understanding and modeling systems with nonlocal interactions; anomalous diffusion and memory effects make them indispensable for addressing modern challenges in applied mathematics and physics. In this paper, the authors introduced a right fractional ( p , q ) $(p,q)$ -integral operator of Riemann–Liouville type, including the q-shifting operator, in parallel to the left fractional ( p , q ) $(p,q)$ -integral operator of Riemann–Liouville type introduced by Neang et al. This is done to investigate the post-quantum multiparameter fundamental identity of continuous functions on finite intervals and to derive some new and existing estimates of various inequalities, such as Bullen type, Simpson type, midpoint type, trapezoid type, etc. In order to verify the accuracy of the findings, graphical and numerical analysis and an application to special means are provided. |
| format | Article |
| id | doaj-art-d47cd1e89ed74dd1bf5a950b701588a1 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-d47cd1e89ed74dd1bf5a950b701588a12025-08-24T11:57:00ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-08-012025113210.1186/s13660-025-03345-zOn post-quantum multiparameter Riemann–Liouville fractional integral inequalities with applicationSobia Rafeeq0Sabir Hussain1Drakhshan Mansab2Hijaz Ahmad3Taha Radwan4Department of Basic Sciences and Humanities (Mathematics), MNS University of Engineering and TechnologyDepartment of Mathematics, University of Engineering and TechnologyDepartment of Mathematics, University of Engineering and TechnologyNear East University, Operational Research Center in Healthcare, Near East BoulevardDepartment of Management Information Systems, College of Business and Economics, Qassim UniversityAbstract Post-quantum integral inequalities involving the Riemann–Liouville fractional integral have a significant role in understanding and modeling systems with nonlocal interactions; anomalous diffusion and memory effects make them indispensable for addressing modern challenges in applied mathematics and physics. In this paper, the authors introduced a right fractional ( p , q ) $(p,q)$ -integral operator of Riemann–Liouville type, including the q-shifting operator, in parallel to the left fractional ( p , q ) $(p,q)$ -integral operator of Riemann–Liouville type introduced by Neang et al. This is done to investigate the post-quantum multiparameter fundamental identity of continuous functions on finite intervals and to derive some new and existing estimates of various inequalities, such as Bullen type, Simpson type, midpoint type, trapezoid type, etc. In order to verify the accuracy of the findings, graphical and numerical analysis and an application to special means are provided.https://doi.org/10.1186/s13660-025-03345-zq-calculusq-shifting operator( p , q ) $(p,q)$ -calculusFractional ( p , q ) $(p,q)$ -integralFractional ( p , q ) $(p,q)$ -integral inequality |
| spellingShingle | Sobia Rafeeq Sabir Hussain Drakhshan Mansab Hijaz Ahmad Taha Radwan On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application Journal of Inequalities and Applications q-calculus q-shifting operator ( p , q ) $(p,q)$ -calculus Fractional ( p , q ) $(p,q)$ -integral Fractional ( p , q ) $(p,q)$ -integral inequality |
| title | On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application |
| title_full | On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application |
| title_fullStr | On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application |
| title_full_unstemmed | On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application |
| title_short | On post-quantum multiparameter Riemann–Liouville fractional integral inequalities with application |
| title_sort | on post quantum multiparameter riemann liouville fractional integral inequalities with application |
| topic | q-calculus q-shifting operator ( p , q ) $(p,q)$ -calculus Fractional ( p , q ) $(p,q)$ -integral Fractional ( p , q ) $(p,q)$ -integral inequality |
| url | https://doi.org/10.1186/s13660-025-03345-z |
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