Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives
We study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order 0<α<1 which can be reduced to Riemann–Liouville or Hadamard fractional derivatives. The existence of mild solu...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1239701 |
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| author | Dussadee Somjaiwang Parinya Sa Ngiamsunthorn |
| author_facet | Dussadee Somjaiwang Parinya Sa Ngiamsunthorn |
| author_sort | Dussadee Somjaiwang |
| collection | DOAJ |
| description | We study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order 0<α<1 which can be reduced to Riemann–Liouville or Hadamard fractional derivatives. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically. In particular, we construct a monotone sequence of functions converging to a solution which is illustrated by a numerical example. |
| format | Article |
| id | doaj-art-1d50824adb014804a7de40e4c0234afe |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1d50824adb014804a7de40e4c0234afe2025-02-03T05:53:49ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1239701Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional DerivativesDussadee Somjaiwang0Parinya Sa Ngiamsunthorn1The Demonstration School of Kanchanaburi Rajabhat UniversityDepartment of MathematicsWe study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order 0<α<1 which can be reduced to Riemann–Liouville or Hadamard fractional derivatives. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically. In particular, we construct a monotone sequence of functions converging to a solution which is illustrated by a numerical example.http://dx.doi.org/10.1155/2022/1239701 |
| spellingShingle | Dussadee Somjaiwang Parinya Sa Ngiamsunthorn Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives Journal of Mathematics |
| title | Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives |
| title_full | Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives |
| title_fullStr | Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives |
| title_full_unstemmed | Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives |
| title_short | Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives |
| title_sort | existence and monotone iterative approximation of solutions for neutral differential equations with generalized fractional derivatives |
| url | http://dx.doi.org/10.1155/2022/1239701 |
| work_keys_str_mv | AT dussadeesomjaiwang existenceandmonotoneiterativeapproximationofsolutionsforneutraldifferentialequationswithgeneralizedfractionalderivatives AT parinyasangiamsunthorn existenceandmonotoneiterativeapproximationofsolutionsforneutraldifferentialequationswithgeneralizedfractionalderivatives |