An extension of picard-lindelöff theorem to fractional differential equations^*

Generation of nonlocal fractional dynamical systems by fractional differential equations

“…Hayek et al [14], hence there are gaps in their proofs of some results, namely the proofs of Theorem 1 on page 71 and of Propositions 1 and 2 on page 72 of [4] are incomplete. For a counter example see Section 6.…”

Fractional differential repetitive processes with Riemann–Liouville and Caputo derivatives

“…They are used, among others things, to the modeling of capacitor (Westerlund and Ekstam 1994;Dzielinski et al 2011Dzielinski et al , 2010, fluid flow through porous material (Langlands 2006), viscoelastic materials (Bagley and Torvik 1986). Fractional systems are investigated in many aspects: existence and uniqueness of solutions (Daftardar-Gejji and Babakhani 2004;Delbosco and Rodino 1996;Hayek et al 1999;Idczak and Kamocki 2011;Kilbas et al 2006), stability and positivity (Buslowicz 2008(Buslowicz , 2011Kaczorek 2011a, b), calculus of variations (Agrawal 2002;Baleanu and Muslih 2005;El-Nabulusi and Torres 2007;Idczak and Majewski 2012;Riewe 1996Riewe , 1997, controllability (Kaczorek 2011c) and optimal control (Agrawal 2004;Jelicic and Petrovacki 2009;Kamocki 2012;Tricaud and Chen 2010).…”

A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation

“…The existence and uniqueness of solutions of IVPs have been studied by many authors [2,[4][5][6][7][8][9][10]. Several methods for solving FDEs are presented in the literature.…”