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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |