Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses
Nonlinear scalar Riemann-Liouville fractional differential equations with a constant delay and impulses are studied and initial conditions and impulsive conditions are set up in an appropriate way. The definitions of both conditions depend significantly on the type of fractional derivative and the p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/607 |
| _version_ | 1797570461522984960 |
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| author | Ravi Agarwal Snezhana Hristova Donal O’Regan |
| author_facet | Ravi Agarwal Snezhana Hristova Donal O’Regan |
| author_sort | Ravi Agarwal |
| collection | DOAJ |
| description | Nonlinear scalar Riemann-Liouville fractional differential equations with a constant delay and impulses are studied and initial conditions and impulsive conditions are set up in an appropriate way. The definitions of both conditions depend significantly on the type of fractional derivative and the presence of the delay in the equation. We study the case of a fixed lower limit of the fractional derivative and the case of a changeable lower limit at each impulsive time. Integral representations of the solutions in all considered cases are obtained. Existence results on finite time intervals are proved using the Banach principle. |
| first_indexed | 2024-03-10T20:25:54Z |
| format | Article |
| id | doaj.art-2cee01763e974f13a72a04e6a9396f37 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:25:54Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2cee01763e974f13a72a04e6a9396f372023-11-19T21:47:12ZengMDPI AGMathematics2227-73902020-04-018460710.3390/math8040607Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and ImpulsesRavi Agarwal0Snezhana Hristova1Donal O’Regan2Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USADepartment of Applied Mathematics and Modeling, University of Plovdiv “Paisii Hilendarski”, 4000 Plovdiv, BulgariaSchool of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 TK33 Galway, IrelandNonlinear scalar Riemann-Liouville fractional differential equations with a constant delay and impulses are studied and initial conditions and impulsive conditions are set up in an appropriate way. The definitions of both conditions depend significantly on the type of fractional derivative and the presence of the delay in the equation. We study the case of a fixed lower limit of the fractional derivative and the case of a changeable lower limit at each impulsive time. Integral representations of the solutions in all considered cases are obtained. Existence results on finite time intervals are proved using the Banach principle.https://www.mdpi.com/2227-7390/8/4/607Riemann-Liouville fractional derivativedelayimpulsesinitial value problemexistence |
| spellingShingle | Ravi Agarwal Snezhana Hristova Donal O’Regan Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses Mathematics Riemann-Liouville fractional derivative delay impulses initial value problem existence |
| title | Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses |
| title_full | Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses |
| title_fullStr | Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses |
| title_full_unstemmed | Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses |
| title_short | Existence and Integral Representation of Scalar Riemann-Liouville Fractional Differential Equations with Delays and Impulses |
| title_sort | existence and integral representation of scalar riemann liouville fractional differential equations with delays and impulses |
| topic | Riemann-Liouville fractional derivative delay impulses initial value problem existence |
| url | https://www.mdpi.com/2227-7390/8/4/607 |
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