Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results. (English) Zbl 1368.34018

de Andrade, Bruno; Carvalho, Alexandre N.; Carvalho-Neto, Paulo M.; Marín-Rubio, Pedro

Topol. Methods Nonlinear Anal. 45, No. 2, 439-467 (2015).

Authors’ abstract: 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.

Reviewer: Samir Bashir Hadid (Ajman)

MSC:

34A08	Fractional ordinary differential equations
34G20	Nonlinear differential equations in abstract spaces
35K05	Heat equation
35R11	Fractional partial differential equations
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

fractional derivatives and integrals; fractional differential equations; nonlinear equations; heat equation