Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results
DOI:
https://doi.org/10.12775/TMNA.2015.022Keywords
Fractional differential equations, semilinear equations, comparison results, critical nonlinearitiesAbstract
In this work we study several questions concerning to abstract fractional Cauchy problems of order $\alpha\in(0,1)$. Concretely, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory.Downloads
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2015-06-01
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CARVALHO, Alexandre Nolasco, CARVALHO-NETO, Paulo M. Carvalho-Neto, MARÍN-RUBIO, Pedro and ANDRADE, Bruno de. Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results. Topological Methods in Nonlinear Analysis. Online. 1 June 2015. Vol. 45, no. 2, pp. 439 - 467. [Accessed 19 April 2024]. DOI 10.12775/TMNA.2015.022.
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