Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations
Mathematics and physics are deeply interconnected. In fact, physics relies on mathematical tools like calculus and differential equations. The aim of this article is to introduce tempered Riemann–Liouville (RL) fractional operators and their properties with applications in mathematical physics. The...
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| Language: | English |
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MDPI AG
2025-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/3/187 |
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| author | Muhammad Umer Muhammad Samraiz Muath Awadalla Meraa Arab |
| author_facet | Muhammad Umer Muhammad Samraiz Muath Awadalla Meraa Arab |
| author_sort | Muhammad Umer |
| collection | DOAJ |
| description | Mathematics and physics are deeply interconnected. In fact, physics relies on mathematical tools like calculus and differential equations. The aim of this article is to introduce tempered Riemann–Liouville (RL) fractional operators and their properties with applications in mathematical physics. The tempered RL substantial fractional derivative is also defined, and its properties are discussed. The Laplace transforms (LTs) of the introduced fractional operators are evaluated. The Hyers–Ulam stability and the existence of a novel tempered fractional differential equation are examined. Moreover, a fractional integro-differential kinetic equation is formulated, and the LT is used to find its solution. A growth model and its graphical representation are established, highlighting the role of novel fractional operators in modeling complex dynamical systems. The developed mathematical framework offers valuable insights into solving a range of scenarios in mathematical physics. |
| format | Article |
| id | doaj-art-b59f164d6652477cb387eb6dff9e6b2a |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-b59f164d6652477cb387eb6dff9e6b2a2025-08-20T02:42:30ZengMDPI AGFractal and Fractional2504-31102025-03-019318710.3390/fractalfract9030187Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic EquationsMuhammad Umer0Muhammad Samraiz1Muath Awadalla2Meraa Arab3Department of Mathematics, University of Sargodha, Sargodha P.O. Box 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha P.O. Box 40100, PakistanDepartment of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Saudi ArabiaMathematics and physics are deeply interconnected. In fact, physics relies on mathematical tools like calculus and differential equations. The aim of this article is to introduce tempered Riemann–Liouville (RL) fractional operators and their properties with applications in mathematical physics. The tempered RL substantial fractional derivative is also defined, and its properties are discussed. The Laplace transforms (LTs) of the introduced fractional operators are evaluated. The Hyers–Ulam stability and the existence of a novel tempered fractional differential equation are examined. Moreover, a fractional integro-differential kinetic equation is formulated, and the LT is used to find its solution. A growth model and its graphical representation are established, highlighting the role of novel fractional operators in modeling complex dynamical systems. The developed mathematical framework offers valuable insights into solving a range of scenarios in mathematical physics.https://www.mdpi.com/2504-3110/9/3/187tempered Riemann–Liouville fractional operatorskinetic integro-differential equationHyers–Ulam stabilityfractional growth model |
| spellingShingle | Muhammad Umer Muhammad Samraiz Muath Awadalla Meraa Arab Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations Fractal and Fractional tempered Riemann–Liouville fractional operators kinetic integro-differential equation Hyers–Ulam stability fractional growth model |
| title | Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations |
| title_full | Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations |
| title_fullStr | Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations |
| title_full_unstemmed | Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations |
| title_short | Tempered Riemann–Liouville Fractional Operators: Stability Analysis and Their Role in Kinetic Equations |
| title_sort | tempered riemann liouville fractional operators stability analysis and their role in kinetic equations |
| topic | tempered Riemann–Liouville fractional operators kinetic integro-differential equation Hyers–Ulam stability fractional growth model |
| url | https://www.mdpi.com/2504-3110/9/3/187 |
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