Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative
By Mohammed D. Kassim, Nasser-Eddine Tatar. 2013
77 citations recorded by the source corpus.
Motivated by the Hilfer fractional derivative (which interpolates the Riemann-Liouville derivative and the Caputo derivative), we consider a new type of fractional derivative (which interpolates the Hadamard derivative and its Caputo counterpart). We prove the well-posedness for a basic Cauchy type fractional differential equation involving this kind of derivative. This is established in an appropriate underlying space after proving the equivalence of this problem with a certain corresponding Volterra integral equation.
Subfields: Applied Mathematics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/cead5190fd3922b4adcdea0edeed7637ee7149f0
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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, result): “We emphasize that our work is new in the present configuration and contributes to the present literature on Hadamard type fractional differential equations and inclusions [41–44].”