Positive solutions of a boundary value problem for a nonlinear fractional differential equation.

By E. Kaufmann, Ebene Mboumi. 2008

698 citations recorded by the source corpus.

In this paper we give sufficient conditions for the existence of at least one and at least three positive solutions to the nonlinear fractional boundary value problem Du + a(t)f(u) = 0, 0 < t < 1,1 < � � 2,

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/ffb8f24dd8c9c6063475bea86131bdf9d45e0db8

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions (2010, background): “... [69], Miller and Ross [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-Ge”
Fractional boundary value problems with singularities in space variables (2012, positive): “There has been a significant development in the study of regular fractional boundary value problems on compact intervals [10–22] and noncompact intervals [23–25].”
Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations (2018, neutral): “From (28), we obtain the following inequality: ||Υ(p, q) − Υ(p∗, q∗)||PC ≤ Q||(p, q) − (p∗, q∗)||PC, (29)”
Variational approach to solutions for a class of fractional Hamiltonian systems (2014, positive): “In this topic, many results are obtained dealing with the existence and multiplicity of solutions of nonlinear fractional differential equations by using techniques of nonlinear analysis, such as fixed point theory (including Leray–Schauder nonlinear alternative [6]), topological degree theory (incl”
EXISTENCE AND UNIQUENESS OF SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS (2009, background): “... in fractional dierential and partial dierential equations in recent years; see the monographs of Kilbas et al [31], Miller and Ross [35], Samko et al [42] and the papers of Agarwal et al [1], Babakhani and Daftardar-Gejji [2, 3], Belmekki et al [6], Benchohra et al [5, 7, 8, 10], Daftardar-Gejji”
Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, background): “Recently, an increasing interest in studying the existence of solutions for boundary value problems of fractional order functional differential equations has been observed [1–10].”
EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS (2008, methodology): “Suppose that tF (t) is continuous function on [0, 1].”