On the analytical and numerical study for fractional q-integrodifferential equations
Abstract In this paper, we give some basic concepts of q-calculus that will be needed in this paper. Then, we built the q-nonlocal condition that ensures the solution existence and uniqueness of the fractional q-integrodifferential equation. Also, we introduce the continuous dependence of the soluti...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-12-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01680-4 |
| _version_ | 1811203700559970304 |
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| author | Amira Abd-Elall Ibrahim Afaf A. S. Zaghrout K. R. Raslan Khalid K. Ali |
| author_facet | Amira Abd-Elall Ibrahim Afaf A. S. Zaghrout K. R. Raslan Khalid K. Ali |
| author_sort | Amira Abd-Elall Ibrahim |
| collection | DOAJ |
| description | Abstract In this paper, we give some basic concepts of q-calculus that will be needed in this paper. Then, we built the q-nonlocal condition that ensures the solution existence and uniqueness of the fractional q-integrodifferential equation. Also, we introduce the continuous dependence of the solution. We find the numerical solution using the finite-difference-Trapezoidal and the cubic B-spline-Trapezoidal methods. Finally, we give three examples to illustrate the validity of our main results. |
| first_indexed | 2024-04-12T02:59:11Z |
| format | Article |
| id | doaj.art-149a9e633a8c41df9d5137fb0de5fd2d |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-12T02:59:11Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-149a9e633a8c41df9d5137fb0de5fd2d2022-12-22T03:50:42ZengSpringerOpenBoundary Value Problems1687-27702022-12-012022111510.1186/s13661-022-01680-4On the analytical and numerical study for fractional q-integrodifferential equationsAmira Abd-Elall Ibrahim0Afaf A. S. Zaghrout1K. R. Raslan2Khalid K. Ali3October High Institute for Engineering and TechnologyMathematics Department, Faculty of Science, Al-Azhar UniversityMathematics Department, Faculty of Science, Al-Azhar UniversityMathematics Department, Faculty of Science, Al-Azhar UniversityAbstract In this paper, we give some basic concepts of q-calculus that will be needed in this paper. Then, we built the q-nonlocal condition that ensures the solution existence and uniqueness of the fractional q-integrodifferential equation. Also, we introduce the continuous dependence of the solution. We find the numerical solution using the finite-difference-Trapezoidal and the cubic B-spline-Trapezoidal methods. Finally, we give three examples to illustrate the validity of our main results.https://doi.org/10.1186/s13661-022-01680-4q-integrodifferential equationExistence and uniqueness of solutionNumerical solutions |
| spellingShingle | Amira Abd-Elall Ibrahim Afaf A. S. Zaghrout K. R. Raslan Khalid K. Ali On the analytical and numerical study for fractional q-integrodifferential equations Boundary Value Problems q-integrodifferential equation Existence and uniqueness of solution Numerical solutions |
| title | On the analytical and numerical study for fractional q-integrodifferential equations |
| title_full | On the analytical and numerical study for fractional q-integrodifferential equations |
| title_fullStr | On the analytical and numerical study for fractional q-integrodifferential equations |
| title_full_unstemmed | On the analytical and numerical study for fractional q-integrodifferential equations |
| title_short | On the analytical and numerical study for fractional q-integrodifferential equations |
| title_sort | on the analytical and numerical study for fractional q integrodifferential equations |
| topic | q-integrodifferential equation Existence and uniqueness of solution Numerical solutions |
| url | https://doi.org/10.1186/s13661-022-01680-4 |
| work_keys_str_mv | AT amiraabdelallibrahim ontheanalyticalandnumericalstudyforfractionalqintegrodifferentialequations AT afafaszaghrout ontheanalyticalandnumericalstudyforfractionalqintegrodifferentialequations AT krraslan ontheanalyticalandnumericalstudyforfractionalqintegrodifferentialequations AT khalidkali ontheanalyticalandnumericalstudyforfractionalqintegrodifferentialequations |