Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law
This research paper intends to study some qualitative analyses for a nonlinear fractional integrodifferential equation with a variable order in the frame of a Mittag-Leffler power law. At first, we convert the considered problem of variable order into an equivalent standard problem of constant order...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6387351 |
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| author | Mdi Begum Jeelani Abeer S. Alnahdi Mohammed A. Almalahi Mohammed S. Abdo Hanan A. Wahash Nadiyah Hussain Alharthi |
| author_facet | Mdi Begum Jeelani Abeer S. Alnahdi Mohammed A. Almalahi Mohammed S. Abdo Hanan A. Wahash Nadiyah Hussain Alharthi |
| author_sort | Mdi Begum Jeelani |
| collection | DOAJ |
| description | This research paper intends to study some qualitative analyses for a nonlinear fractional integrodifferential equation with a variable order in the frame of a Mittag-Leffler power law. At first, we convert the considered problem of variable order into an equivalent standard problem of constant order using generalized intervals and piecewise constant functions. Next, we prove the existence and uniqueness of analytic results by application of Krasnoselskii’s and Banach’s fixed point theorems. Besides, the guarantee of the existence of solutions is shown by different types of Ulam-Hyer’s stability. Then, we investigate sufficient conditions of positive solutions for the proposed problem. In the end, we discuss an example to illustrate the applicability of our obtained results. |
| format | Article |
| id | doaj-art-f444f440f47b4efd9e95f93e44b34763 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-f444f440f47b4efd9e95f93e44b347632025-02-03T01:22:44ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6387351Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power LawMdi Begum Jeelani0Abeer S. Alnahdi1Mohammed A. Almalahi2Mohammed S. Abdo3Hanan A. Wahash4Nadiyah Hussain Alharthi5Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematics and StatisticsThis research paper intends to study some qualitative analyses for a nonlinear fractional integrodifferential equation with a variable order in the frame of a Mittag-Leffler power law. At first, we convert the considered problem of variable order into an equivalent standard problem of constant order using generalized intervals and piecewise constant functions. Next, we prove the existence and uniqueness of analytic results by application of Krasnoselskii’s and Banach’s fixed point theorems. Besides, the guarantee of the existence of solutions is shown by different types of Ulam-Hyer’s stability. Then, we investigate sufficient conditions of positive solutions for the proposed problem. In the end, we discuss an example to illustrate the applicability of our obtained results.http://dx.doi.org/10.1155/2022/6387351 |
| spellingShingle | Mdi Begum Jeelani Abeer S. Alnahdi Mohammed A. Almalahi Mohammed S. Abdo Hanan A. Wahash Nadiyah Hussain Alharthi Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law Journal of Function Spaces |
| title | Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law |
| title_full | Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law |
| title_fullStr | Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law |
| title_full_unstemmed | Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law |
| title_short | Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law |
| title_sort | qualitative analyses of fractional integrodifferential equations with a variable order under the mittag leffler power law |
| url | http://dx.doi.org/10.1155/2022/6387351 |
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