Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method
Abstract A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives are replaced by the Caputo operator, and the solution is demonstrated by the hybr...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-03-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2044-1 |
| _version_ | 1818033464006410240 |
|---|---|
| author | Mohamed R. Ali Adel R. Hadhoud H. M. Srivastava |
| author_facet | Mohamed R. Ali Adel R. Hadhoud H. M. Srivastava |
| author_sort | Mohamed R. Ali |
| collection | DOAJ |
| description | Abstract A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives are replaced by the Caputo operator, and the solution is demonstrated by the hybrid orthonormal Bernstein and block-pulse functions wavelet method (HOBW). We demonstrate the convergence analysis for this technique to emphasize its reliability. The applicability of the HOBW is demonstrated using three examples. The approximate results of this technique are compared with the correct solutions, which shows that this technique has approval with the correct solutions to the problems. |
| first_indexed | 2024-12-10T06:23:40Z |
| format | Article |
| id | doaj.art-ddb0078c03de45dcb3688b2894fd3251 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T06:23:40Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-ddb0078c03de45dcb3688b2894fd32512022-12-22T01:59:16ZengSpringerOpenAdvances in Difference Equations1687-18472019-03-012019111410.1186/s13662-019-2044-1Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW methodMohamed R. Ali0Adel R. Hadhoud1H. M. Srivastava2Department of Mathematics, Benha Faculty of Engineering, Benha UniversityDepartment of Mathematics, Faculty of Science, Menoufia UniversityDepartment of Mathematics and Statistics, University of VictoriaAbstract A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives are replaced by the Caputo operator, and the solution is demonstrated by the hybrid orthonormal Bernstein and block-pulse functions wavelet method (HOBW). We demonstrate the convergence analysis for this technique to emphasize its reliability. The applicability of the HOBW is demonstrated using three examples. The approximate results of this technique are compared with the correct solutions, which shows that this technique has approval with the correct solutions to the problems.http://link.springer.com/article/10.1186/s13662-019-2044-1Orthonormal BernsteinBlock-pulse functionsWavelet methodFractional integro-differential equationsFractional calculusApproximate solution |
| spellingShingle | Mohamed R. Ali Adel R. Hadhoud H. M. Srivastava Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method Advances in Difference Equations Orthonormal Bernstein Block-pulse functions Wavelet method Fractional integro-differential equations Fractional calculus Approximate solution |
| title | Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method |
| title_full | Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method |
| title_fullStr | Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method |
| title_full_unstemmed | Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method |
| title_short | Solution of fractional Volterra–Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method |
| title_sort | solution of fractional volterra fredholm integro differential equations under mixed boundary conditions by using the hobw method |
| topic | Orthonormal Bernstein Block-pulse functions Wavelet method Fractional integro-differential equations Fractional calculus Approximate solution |
| url | http://link.springer.com/article/10.1186/s13662-019-2044-1 |
| work_keys_str_mv | AT mohamedrali solutionoffractionalvolterrafredholmintegrodifferentialequationsundermixedboundaryconditionsbyusingthehobwmethod AT adelrhadhoud solutionoffractionalvolterrafredholmintegrodifferentialequationsundermixedboundaryconditionsbyusingthehobwmethod AT hmsrivastava solutionoffractionalvolterrafredholmintegrodifferentialequationsundermixedboundaryconditionsbyusingthehobwmethod |