Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions

By Anatoly A. Kilbas, S. Marzan. 2005

276 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/18f8276f0963f1507357dd636fc8d5593f878e0a

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Method of upper and lower solutions for fractional differential equations (2012, background): “Hence, some meaningful results on this kind of problems have been obtained, (see [5, 6, 7, 8, 9, 10, 11, 12, 13]).”
On fractional order derivatives and Darboux problem for implicit differential equations (2012, background): “[15] A.A. Kilbas and S.A. Marzan, Cauchy problem for differential equation with Caputo derivative, Fract.”
Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions. (2010, background): “Furati and Tatar [28, 29], Kaufmann and Mboumi [36], Kilbas and Marzan [37], Mainardi [40], Momani and Hadid [43], Momani et al.”
Boundary Value Problems for Differential Equations Involving Riemann-Liouville Fractional Derivative on the Half-Line (2011, background): “[18], Podlubny [21], Samko et al [23] and the papers by Agarwal et al [1], Delbosco and Rodino [9], Diethelm et al [10], Kilbas and Marzan [16], Mainardi [19], Zhang [24] and the references therein.”
Existence results for boundary value problems with non-linear fractional differential equations (2008, background): “3 [20] For a function h given on the interval [a, b], the Caputo fractionalorder derivative of h, is defined by ðD aþhÞðtÞ 1⁄4 1 ðn Þ Z t”
Positive solutions of a boundary value problem for a nonlinear fractional differential equation. (2008, methodology): “While much attention has focused on the Cauchy problem for fractional differential equations for both the Reimann-Liouville and Caputo differential operators, see [8, 17, 24 , 28, 29, 30, 31, 32, 34] and references therein, there are few papers devoted to the study of fractional order boundary valu”
EXISTENCE AND UNIQUENESS OF SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS (2009, unknown): “3, 11 pp. [30] A. A. Kilbas and S. A. Marzan; Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, Differential Equations 41 (2005), 84-89.”
A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions (2010, background): “... [75], Samko et al. [85] and the papers of Agarwal et al. [2–6], Ait Dads et al. [8], Babakhani and Daftardar-Gejji [11, 12], Belmekki et al. [17, 18], Benchohra et al. [25–27, 29], Benchohra and Hamani [19, 20], Benchohra and Slimani [21], Chang and Nieto [38], Daftardar-Gejji and Jafari [40, 41”