Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
Abstract In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. T...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03631-2 |
| _version_ | 1818897322663215104 |
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| author | Mohammad Esmael Samei Ahmad Ahmadi A. George Maria Selvam Jehad Alzabut Shahram Rezapour |
| author_facet | Mohammad Esmael Samei Ahmad Ahmadi A. George Maria Selvam Jehad Alzabut Shahram Rezapour |
| author_sort | Mohammad Esmael Samei |
| collection | DOAJ |
| description | Abstract In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings. |
| first_indexed | 2024-12-19T19:14:20Z |
| format | Article |
| id | doaj.art-287958b78b32476e807cc7c7ecfc6e81 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T19:14:20Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-287958b78b32476e807cc7c7ecfc6e812022-12-21T20:09:11ZengSpringerOpenAdvances in Difference Equations1687-18472021-11-012021112610.1186/s13662-021-03631-2Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theoremMohammad Esmael Samei0Ahmad Ahmadi1A. George Maria Selvam2Jehad Alzabut3Shahram Rezapour4Department of Mathematics, Bu-Ali Sina UniversityDepartment of Mathematics, Bu-Ali Sina UniversityDepartment of Mathematics, Sacred Heart College (Autonomous)Department of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, Azarbaijan Shahid Madani UniversityAbstract In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.https://doi.org/10.1186/s13662-021-03631-2Fractional q-derivative equationsNonlinear analysis theoremsWell-posedness |
| spellingShingle | Mohammad Esmael Samei Ahmad Ahmadi A. George Maria Selvam Jehad Alzabut Shahram Rezapour Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem Advances in Difference Equations Fractional q-derivative equations Nonlinear analysis theorems Well-posedness |
| title | Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem |
| title_full | Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem |
| title_fullStr | Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem |
| title_full_unstemmed | Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem |
| title_short | Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem |
| title_sort | well posed conditions on a class of fractional q differential equations by using the schauder fixed point theorem |
| topic | Fractional q-derivative equations Nonlinear analysis theorems Well-posedness |
| url | https://doi.org/10.1186/s13662-021-03631-2 |
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