Cauchy problem for fractional $ {(p, q)} $-difference equations
In this research article, we deal with the global convergence of successive approximations (s.a) as well as the existence of solutions to a fractional $ {(p, q)} $-difference equation. Then, we discuss the existence result of the solutions of Caputo-type $ {(p, q)} $-difference fractional vector-ord...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-04-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023805?viewType=HTML |
| _version_ | 1797824617697509376 |
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| author | Abdelatif Boutiara Mohamed Rhaima Lassaad Mchiri Abdellatif Ben Makhlouf |
| author_facet | Abdelatif Boutiara Mohamed Rhaima Lassaad Mchiri Abdellatif Ben Makhlouf |
| author_sort | Abdelatif Boutiara |
| collection | DOAJ |
| description | In this research article, we deal with the global convergence of successive approximations (s.a) as well as the existence of solutions to a fractional $ {(p, q)} $-difference equation. Then, we discuss the existence result of the solutions of Caputo-type $ {(p, q)} $-difference fractional vector-order equations in a Banach space. Also, we prove a theorem on the global convergence of successive approximations to the unique solution of our problem. Finally, the application of the main results is demonstrated by presenting numerical examples. |
| first_indexed | 2024-03-13T10:41:39Z |
| format | Article |
| id | doaj.art-0a77ef41ecb2439cb3c25e2014e0dea9 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T10:41:39Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0a77ef41ecb2439cb3c25e2014e0dea92023-05-18T02:37:29ZengAIMS PressAIMS Mathematics2473-69882023-04-0187157731578810.3934/math.2023805Cauchy problem for fractional $ {(p, q)} $-difference equationsAbdelatif Boutiara0Mohamed Rhaima1Lassaad Mchiri2Abdellatif Ben Makhlouf 31. Department of Mathematics and Computer Science, University of Ghardaia, BP 455 Ghardaia 47000, Algeria2. Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia3. ENSIIE, University of Evry-Val-d'Essonne, 1 square de la Résistance 91025 Évry-Courcouronnes cedex, France4. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, TunisiaIn this research article, we deal with the global convergence of successive approximations (s.a) as well as the existence of solutions to a fractional $ {(p, q)} $-difference equation. Then, we discuss the existence result of the solutions of Caputo-type $ {(p, q)} $-difference fractional vector-order equations in a Banach space. Also, we prove a theorem on the global convergence of successive approximations to the unique solution of our problem. Finally, the application of the main results is demonstrated by presenting numerical examples.https://www.aimspress.com/article/doi/10.3934/math.2023805?viewType=HTMLfractional $ {(pq)} $-calculusglobal convergencesuccessive approximationsmeasure of non-compactnessmeir-keeler condensing operators |
| spellingShingle | Abdelatif Boutiara Mohamed Rhaima Lassaad Mchiri Abdellatif Ben Makhlouf Cauchy problem for fractional $ {(p, q)} $-difference equations AIMS Mathematics fractional $ {(p q)} $-calculus global convergence successive approximations measure of non-compactness meir-keeler condensing operators |
| title | Cauchy problem for fractional $ {(p, q)} $-difference equations |
| title_full | Cauchy problem for fractional $ {(p, q)} $-difference equations |
| title_fullStr | Cauchy problem for fractional $ {(p, q)} $-difference equations |
| title_full_unstemmed | Cauchy problem for fractional $ {(p, q)} $-difference equations |
| title_short | Cauchy problem for fractional $ {(p, q)} $-difference equations |
| title_sort | cauchy problem for fractional p q difference equations |
| topic | fractional $ {(p q)} $-calculus global convergence successive approximations measure of non-compactness meir-keeler condensing operators |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023805?viewType=HTML |
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