On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator
Abstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differenti...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-06-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03459-w |
| _version_ | 1797831908724310016 |
|---|---|
| author | Muhammad Aleem Mujeeb Ur Rehman Jehad Alzabut Sina Etemad Shahram Rezapour |
| author_facet | Muhammad Aleem Mujeeb Ur Rehman Jehad Alzabut Sina Etemad Shahram Rezapour |
| author_sort | Muhammad Aleem |
| collection | DOAJ |
| description | Abstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differential equations with Riemann–Liouville, Caputo, and classical Riesz derivative. Some special cases can be derived to obtain corresponding existence results for fractional differential equations. We provide an illustrated example for the unique solution of our main result. |
| first_indexed | 2024-04-09T14:00:24Z |
| format | Article |
| id | doaj.art-c6c0d0faeabe4d8d85e83476f00b5cc9 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-09T14:00:24Z |
| publishDate | 2021-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-c6c0d0faeabe4d8d85e83476f00b5cc92023-05-07T11:23:19ZengSpringerOpenAdvances in Difference Equations1687-18472021-06-012021112810.1186/s13662-021-03459-wOn solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operatorMuhammad Aleem0Mujeeb Ur Rehman1Jehad Alzabut2Sina Etemad3Shahram Rezapour4School of Natural Sciences, National University of Sciences and TechnologySchool of Natural Sciences, National University of Sciences and TechnologyDepartment of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, Azarbaijan Shahid Madani UniversityDepartment of Mathematics, Azarbaijan Shahid Madani UniversityAbstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class of fractional differential equations by using a generalized Riesz fractional operator. One can view the results of this work as a refinement for the existence theory of fractional differential equations with Riemann–Liouville, Caputo, and classical Riesz derivative. Some special cases can be derived to obtain corresponding existence results for fractional differential equations. We provide an illustrated example for the unique solution of our main result.https://doi.org/10.1186/s13662-021-03459-wFixed point theoryGronwall inequalityStability of solutionsThe generalized Riesz fractional operatorThe generalized Caputo fractional operator |
| spellingShingle | Muhammad Aleem Mujeeb Ur Rehman Jehad Alzabut Sina Etemad Shahram Rezapour On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator Advances in Difference Equations Fixed point theory Gronwall inequality Stability of solutions The generalized Riesz fractional operator The generalized Caputo fractional operator |
| title | On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator |
| title_full | On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator |
| title_fullStr | On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator |
| title_full_unstemmed | On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator |
| title_short | On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator |
| title_sort | on solutions of nonlinear bvps with general boundary conditions by using a generalized riesz caputo operator |
| topic | Fixed point theory Gronwall inequality Stability of solutions The generalized Riesz fractional operator The generalized Caputo fractional operator |
| url | https://doi.org/10.1186/s13662-021-03459-w |
| work_keys_str_mv | AT muhammadaleem onsolutionsofnonlinearbvpswithgeneralboundaryconditionsbyusingageneralizedrieszcaputooperator AT mujeeburrehman onsolutionsofnonlinearbvpswithgeneralboundaryconditionsbyusingageneralizedrieszcaputooperator AT jehadalzabut onsolutionsofnonlinearbvpswithgeneralboundaryconditionsbyusingageneralizedrieszcaputooperator AT sinaetemad onsolutionsofnonlinearbvpswithgeneralboundaryconditionsbyusingageneralizedrieszcaputooperator AT shahramrezapour onsolutionsofnonlinearbvpswithgeneralboundaryconditionsbyusingageneralizedrieszcaputooperator |