Fractional Sobolev Spaces via Riemann-Liouville Derivatives

By D. Idczak, S. Walczak. 2013

54 citations recorded by the source corpus.

Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of some imbeddings. An application to boundary value problems is given as well.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7bbb77a060c7a5a86286db6f41e5a80f5b9b5a9e

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In Applied Mathematics

1. Stepan A. Tersian
2. Gabriele Bonanno
3. Rosana Rodríguez-López
4. Pasquale Candito
5. Giuseppina D'Aguì
6. Diego Averna
7. Bessem Samet
8. Vasile Berinde

In Modeling and Simulation

1. Stepan A. Tersian
2. Rosana Rodríguez-López
3. Gabriele Bonanno
4. Diego Averna

Citations in the corpus

• Existence of solutions to boundary value problem for impulsive fractional differential equations (2014, background): “For further properties of fractional Sobolev spaces we refer to [15].”