Agarwal, Ravi P.; Benchohra, Mouffak; Slimani, Boualem Attou Existence results for differential equations with fractional order and impulses. (English) Zbl 1178.26006 Mem. Differ. Equ. Math. Phys. 44, 1-21 (2008). The authors study the fractional differential equation \[ D^\alpha y(t)=f(t,y), \;\;t\in [0,T], \;\;1<\alpha\leq 2 \] where \(D^\alpha y\) is the Caputo fractional derivative, in the setting where \(y(t)\) is allowed to have jumps at a given set \(\{t_1,...,t_m\}\subset [0,T]\). They prove three versions of the existence and uniqueness theorem for this equation under the initial conditions \(y(0)=y_0, y^\prime(0)=y_1\), and a set of conditions on jumps of \(y(t)\) and \(y^\prime(t)\) at the points \(t_1,...,t_m.\) Reviewer: Stefan G. Samko (Faro) Cited in 1 ReviewCited in 77 Documents MSC: 26A33 Fractional derivatives and integrals Keywords:fractional differential equation; Caputo fractional derivative PDFBibTeX XMLCite \textit{R. P. Agarwal} et al., Mem. Differ. Equ. Math. Phys. 44, 1--21 (2008; Zbl 1178.26006)