On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation
We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solutio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/3276873 |
| Summary: | We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results. |
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| ISSN: | 1024-123X 1563-5147 |