Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order
Abstract This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03042-9 |
| _version_ | 1797451138591621120 |
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| author | Kheireddine Benia Mohammed Said Souid Fahd Jarad Manar A. Alqudah Thabet Abdeljawad |
| author_facet | Kheireddine Benia Mohammed Said Souid Fahd Jarad Manar A. Alqudah Thabet Abdeljawad |
| author_sort | Kheireddine Benia |
| collection | DOAJ |
| description | Abstract This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam–Hyers–Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results. |
| first_indexed | 2024-03-09T14:49:29Z |
| format | Article |
| id | doaj.art-91e2459ac44d49e189cceb60f854d5d2 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-09T14:49:29Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-91e2459ac44d49e189cceb60f854d5d22023-11-26T14:32:39ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-10-012023111610.1186/s13660-023-03042-9Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable orderKheireddine Benia0Mohammed Said Souid1Fahd Jarad2Manar A. Alqudah3Thabet Abdeljawad4Departement of Mathematics, Ibn Khaldoun UniversityDepartment of Economic Sciences, Ibn Khaldoun UniversityDepartment of Mathematics, Faculty of Arts and Science, Çankaya UnivDept Math Sci, Fac Sci, Princess Nourah Bint Abdulrahman UnivDepartment of Mathematics and Sciences, Prince Sultan UniversityAbstract This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam–Hyers–Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.https://doi.org/10.1186/s13660-023-03042-9Weighted fractional integralsWeighted spaces of summable functionsFixed point theoremDerivatives and integrals of variable orderBoundary value problemMeasure of non-compactness |
| spellingShingle | Kheireddine Benia Mohammed Said Souid Fahd Jarad Manar A. Alqudah Thabet Abdeljawad Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order Journal of Inequalities and Applications Weighted fractional integrals Weighted spaces of summable functions Fixed point theorem Derivatives and integrals of variable order Boundary value problem Measure of non-compactness |
| title | Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order |
| title_full | Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order |
| title_fullStr | Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order |
| title_full_unstemmed | Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order |
| title_short | Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order |
| title_sort | boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order |
| topic | Weighted fractional integrals Weighted spaces of summable functions Fixed point theorem Derivatives and integrals of variable order Boundary value problem Measure of non-compactness |
| url | https://doi.org/10.1186/s13660-023-03042-9 |
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