On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation
In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></seman...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4821 |
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| author | Abdelkrim Salim Jehad Alzabut Weerawat Sudsutad Chatthai Thaiprayoon |
| author_facet | Abdelkrim Salim Jehad Alzabut Weerawat Sudsutad Chatthai Thaiprayoon |
| author_sort | Abdelkrim Salim |
| collection | DOAJ |
| description | In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle and Krasnoselskii’s fixed point theorem. In addition, the Ulam–Hyers–Rassias stability result is proved using the nonlinear functional analysis technique. Finally, illustrative examples are given to validate our main results. |
| first_indexed | 2024-03-09T16:08:12Z |
| format | Article |
| id | doaj.art-7e325b4207b345b4b855e29b36b035f7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:08:12Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7e325b4207b345b4b855e29b36b035f72023-11-24T16:30:20ZengMDPI AGMathematics2227-73902022-12-011024482110.3390/math10244821On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and AnticipationAbdelkrim Salim0Jehad Alzabut1Weerawat Sudsutad2Chatthai Thaiprayoon3Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, AlgeriaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaTheoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, ThailandResearch Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, ThailandIn this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle and Krasnoselskii’s fixed point theorem. In addition, the Ulam–Hyers–Rassias stability result is proved using the nonlinear functional analysis technique. Finally, illustrative examples are given to validate our main results.https://www.mdpi.com/2227-7390/10/24/4821fixed point theoremψ-Caputo fractional derivativeexistence and uniquenessUlam–Hyers–Rassias stabilitynon-instantaneous impulses |
| spellingShingle | Abdelkrim Salim Jehad Alzabut Weerawat Sudsutad Chatthai Thaiprayoon On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation Mathematics fixed point theorem ψ-Caputo fractional derivative existence and uniqueness Ulam–Hyers–Rassias stability non-instantaneous impulses |
| title | On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation |
| title_full | On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation |
| title_fullStr | On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation |
| title_full_unstemmed | On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation |
| title_short | On Impulsive Implicit <i>ψ</i>-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation |
| title_sort | on impulsive implicit i ψ i caputo hybrid fractional differential equations with retardation and anticipation |
| topic | fixed point theorem ψ-Caputo fractional derivative existence and uniqueness Ulam–Hyers–Rassias stability non-instantaneous impulses |
| url | https://www.mdpi.com/2227-7390/10/24/4821 |
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