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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01754 |
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Table of Contents:
- We prove the existence and uniqueness of mild solutions for a specific class of time-fractional $ψ$-Caputo evolution systems with a derivative order ranging from 1 to 2 in Banach spaces. By using the properties of cosine and sine family operators, along with the generalized Laplace transform, we derive a more concise expression for the mild solution. This expression is formulated as an integral, incorporating Mainardi's Wright-type function. Furthermore, we provide various valuable properties associated with the operators present in the mild solution. Additionally, employing the fixed-point technique and Grönwall's inequality, we establish the existence and uniqueness of the mild solution. To illustrate our results, we conclude with an example of a time-fractional equation, presenting the expression for its corresponding mild solution.