Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness
This paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo’s fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam–Hy...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/1/80 |
| _version_ | 1797446162213502976 |
|---|---|
| author | Benoumran Telli Mohammed Said Souid Ivanka Stamova |
| author_facet | Benoumran Telli Mohammed Said Souid Ivanka Stamova |
| author_sort | Benoumran Telli |
| collection | DOAJ |
| description | This paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo’s fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam–Hyers stability criteria are examined. All of the results in this study are established with the help of generalized intervals and piecewise constant functions. We convert the Riemann–Liouville fractional variable-order problem to equivalent standard Riemann–Liouville problems of fractional-constant orders. Finally, two examples are constructed to illustrate the validity of the observed results. |
| first_indexed | 2024-03-09T13:36:15Z |
| format | Article |
| id | doaj.art-a71e99694e6244ff82cea9782e0fe2f3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:36:15Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-a71e99694e6244ff82cea9782e0fe2f32023-11-30T21:12:02ZengMDPI AGAxioms2075-16802023-01-011218010.3390/axioms12010080Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of NoncompactnessBenoumran Telli0Mohammed Said Souid1Ivanka Stamova2Department of Mathematics, University of Tiaret, Tiaret 14035, AlgeriaDepartment of Economic Sciences, University of Tiaret, Tiaret 14035, AlgeriaDepartment of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USAThis paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo’s fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam–Hyers stability criteria are examined. All of the results in this study are established with the help of generalized intervals and piecewise constant functions. We convert the Riemann–Liouville fractional variable-order problem to equivalent standard Riemann–Liouville problems of fractional-constant orders. Finally, two examples are constructed to illustrate the validity of the observed results.https://www.mdpi.com/2075-1680/12/1/80fractional differential equations of variable orderfinite delayboundary-value problemfixed-point theoremgreen functionUlam–Hyers stability |
| spellingShingle | Benoumran Telli Mohammed Said Souid Ivanka Stamova Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness Axioms fractional differential equations of variable order finite delay boundary-value problem fixed-point theorem green function Ulam–Hyers stability |
| title | Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness |
| title_full | Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness |
| title_fullStr | Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness |
| title_full_unstemmed | Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness |
| title_short | Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness |
| title_sort | boundary value problem for nonlinear fractional differential equations of variable order with finite delay via kuratowski measure of noncompactness |
| topic | fractional differential equations of variable order finite delay boundary-value problem fixed-point theorem green function Ulam–Hyers stability |
| url | https://www.mdpi.com/2075-1680/12/1/80 |
| work_keys_str_mv | AT benoumrantelli boundaryvalueproblemfornonlinearfractionaldifferentialequationsofvariableorderwithfinitedelayviakuratowskimeasureofnoncompactness AT mohammedsaidsouid boundaryvalueproblemfornonlinearfractionaldifferentialequationsofvariableorderwithfinitedelayviakuratowskimeasureofnoncompactness AT ivankastamova boundaryvalueproblemfornonlinearfractionaldifferentialequationsofvariableorderwithfinitedelayviakuratowskimeasureofnoncompactness |