The \(e\)-positive mild solutions for impulsive evolution fractional differential equations with sectorial operator. (English) Zbl 07812182
Summary: In this paper, we investigate the existence of global \(e\)-positive mild solutions to the initial value problem for a nonlinear impulsive fractional evolution differential equation involving the theory of sectorial operators. To obtain the result, we used Kuratowski’s non-compactness measure theory, the Cauchy criterion and the Gronwall inequality.
MSC:
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34A08 | Fractional ordinary differential equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 34A47 | Bifurcation (MSC1991) |
Keywords:
fractional impulsive evolution equations; global \(e\)-positive mild solutions; Gronwall inequality; measure noncompactnessReferences:
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| [46] | Jorge F. Junior Department of Applied Mathematics Imecc-State University of Campinas 13083-859, Campinas, SP, Brazil e-mail: ra898061@ime.unicamp.br J. Vanterler da C. Sousa Department of Applied Mathematics Imecc-State University of Campinas 13083-859, Campinas, SP, Brazil e-mail: vanterler@ime.unicamp.br E. Capelas de Oliveira Department of Applied Mathematics Imecc-State University of Campinas 13083-859, Campinas, SP, Brazil e-mail: capelas@unicamp.br Differential Equations & Applications www.ele-math.com dea@ele-math.com |
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