Extremal solutions of φ−Caputo fractional evolution equations involving integral kernels
| Autor: | Parinya Sa Ngiamsunthorn, Apassara Suechoei |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Volterra operator
Semigroup General Mathematics Fredholm operator volterra operator lcsh:Mathematics fredholm operator upper and lower solutions lcsh:QA1-939 Fractional calculus fractional evolution equation Nonlinear system Monotone polygon Applied mathematics Initial value problem monotone iterative technique Uniqueness Mathematics |
| Zdroj: | AIMS Mathematics, Vol 6, Iss 5, Pp 4734-4757 (2021) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2021278?viewType=HTML |
| Popis: | This paper deals with the existence and uniqueness of solution for the Cauchy problem of $ \varphi- $Caputo fractional evolution equations involving Volterra and Fredholm integral kernels. We derive a mild solution in terms of semigroup and construct a monotone iterative sequence for extremal solutions under a noncompactness measure condition of the nonlinearity. These results can be reduced to previous works with the classical Caputo fractional derivative. Furthermore, we give an example of initial-boundary value problem for the time-fractional parabolic equation to illustrate the application of the results. |
| Databáze: | OpenAIRE |
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