References

The following lists the core references involved in the study of combinations of fractional differential operators and function spaces.

Journal Papers & Monographs

  1. Sakamoto, K., & Yamamoto, M. (2011). "Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems." Journal of Mathematical Analysis and Applications, 382(1), 426-447.
  2. Ros-Oton, X., & Serra, J. (2014). "The Dirichlet problem for the fractional Laplacian: regularity up to the boundary." Journal de Mathématiques Pures et Appliquées, 101(3), 275-302.
  3. Caffarelli, L., & Silvestre, L. (2009). "Regularity theory for fully nonlinear integro-differential equations." Communications on Pure and Applied Mathematics, 62(5), 597-638.
  4. Cabré, X., & Tan, J. (2010). "Positive solutions of nonlinear problems involving the square root of the Laplacian." Advances in Mathematics, 224(5), 2052-2093.
  5. Mainardi, F., Luchko, Y., & Pagnini, G. (2001). "The fundamental solution of the space-time fractional diffusion equation." Fractional Calculus and Applied Analysis, 4(2), 153-192.
  6. Franzina, G., & Palatucci, G. (2014). "Fractional p-eigenvalues." Rivista di Matematica della Università di Parma, 5(2), 373-386.
  7. Grubb, G. (2026). "The structure of solution spaces for fractional-order operators, with gradient estimates." arXiv:2607.02312.
  8. Kochubei, A. N. (2008). "Distributed order calculus and equations of ultraslow diffusion." Journal of Mathematical Analysis and Applications, 340(1), 252-281.
  9. Acerbi, E., & Mingione, G. (2002). "Regularity results for stationary electro-rheological fluids." Archive for Rational Mechanics and Analysis, 164(3), 213-259.

Classic Monographs

  1. Samko, S. G., Kilbas, A. A., & Marichev, O. I. (1993). Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers.
  2. Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier.
  3. Podlubny, I. (1999). Fractional Differential Equations. Academic Press.