APPLICATION OF THE MIXED MONOTONE OPERATOR METHOD TO FRACTIONAL BOUNDARY VALUE PROBLEMS
By John R. Graef, Lingju Kong, Qingkai Kong. 2012
47 citations recorded by the source corpus.
The authors use the mixed monotone operator method to study the fractional boundary value problem −D ν+ u(t )= λ f (t, u), t ∈ (0,1), u (j) (0 )= 0, j = 0,...,n −2, (D α+ u(t))t=1 = 0. Here, m 1a ndn 3 are integers, n −1 < ν n ,1 α n −2, u(t)=(u1(t),...,um(t)) T , λ =(λ1,...,λm), λ f (t, u)=(λ1 f1(t, u),...,λm fm(t, u)) T ,a ndD ν+ is the Riemann-Liouville fractional derivative of order ν . Existence, uniqueness, and dependence of positive solutions on the parameter λ are discussed. An application to a special problem is also presented.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/a1201c3761dce6e13e67e038c88ba5484943c649
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In Applied Mathematics
- Sotiris K. Ntouyas
- Bashir Ahmad
- J. J. Nieto
- Jinrong Wang
- Yong Zhou
- Ahmed Alsaedi
- Gennaro Infante
- Paolamaria Pietramala
In Modeling and Simulation
- Sotiris K. Ntouyas
- Bashir Ahmad
- Ahmed Alsaedi
- J. J. Nieto
- Yong Zhou
- Gennaro Infante
- Jinrong Wang
- Paolamaria Pietramala
Citations in the corpus
- An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions (2014, background): “Much of the work on fractional differential equations involves either Riemann-Liouville derivative or Caputo derivative; for instance, see [4–33] and the references therein.”