The Existence and Stability of Integral Fractional Differential Equations
The main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the prerequisites for the existence and uniqueness of the solut...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/295 |
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| author | Rahman Ullah Khan Ioan-Lucian Popa |
| author_facet | Rahman Ullah Khan Ioan-Lucian Popa |
| author_sort | Rahman Ullah Khan |
| collection | DOAJ |
| description | The main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the prerequisites for the existence and uniqueness of the solutions. The Schauder fixed-point theorem and the Banach contraction principle are employed to obtain the results. Finally, we present an example to demonstrate the practical application of our theoretical conclusions. |
| format | Article |
| id | doaj-art-eabe6de967e04dc6bcfd30f52aed3912 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-eabe6de967e04dc6bcfd30f52aed39122025-08-20T03:47:59ZengMDPI AGFractal and Fractional2504-31102025-05-019529510.3390/fractalfract9050295The Existence and Stability of Integral Fractional Differential EquationsRahman Ullah Khan0Ioan-Lucian Popa1Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, RomaniaThe main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the prerequisites for the existence and uniqueness of the solutions. The Schauder fixed-point theorem and the Banach contraction principle are employed to obtain the results. Finally, we present an example to demonstrate the practical application of our theoretical conclusions.https://www.mdpi.com/2504-3110/9/5/295integral fractional differential equationABC-fractional derivativefixed-point theoremsstability |
| spellingShingle | Rahman Ullah Khan Ioan-Lucian Popa The Existence and Stability of Integral Fractional Differential Equations Fractal and Fractional integral fractional differential equation ABC-fractional derivative fixed-point theorems stability |
| title | The Existence and Stability of Integral Fractional Differential Equations |
| title_full | The Existence and Stability of Integral Fractional Differential Equations |
| title_fullStr | The Existence and Stability of Integral Fractional Differential Equations |
| title_full_unstemmed | The Existence and Stability of Integral Fractional Differential Equations |
| title_short | The Existence and Stability of Integral Fractional Differential Equations |
| title_sort | existence and stability of integral fractional differential equations |
| topic | integral fractional differential equation ABC-fractional derivative fixed-point theorems stability |
| url | https://www.mdpi.com/2504-3110/9/5/295 |
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