INVERSE PROBLEMS FOR GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL-ORDER DIFFERENTIAL OPERATORS
Keywords:
Fractional calculus, Riemann-Liouville, Inverse problem, Existence, Uniqueness, Nonlocal, RegularizationAbstract
This chapter investigates the fundamental aspects of inverse problems for fractional-order generalized Riemann-Liouville differential operator equations. It analyzes the history, properties, and role of the Riemann-Liouville integral in fractional differentiation. The theoretical foundations of inverse problems, encompassing existence, uniqueness, and solution methods for fractional operators, are synthesized from modern research. Challenges arising from the non-local nature and lack of classical tools are elucidated, alongside a discussion of the research methodology, potential outcomes, and future research avenues.
Downloads
References
Podlubny, I. Fractional Differential Equations. San Diego: Academic Press, 1999.
Isakov, V. Inverse Problems for Partial Differential Equations. New York: Springer, 2017.
Luchko, Y. "An inverse source problem for the time-fractional diffusion equation." Inverse Problems, vol. 34, no. 6, 2018, 065005.
Cheng, J., Nakagawa, J., Yamamoto, M. "An inverse problem for a fractional diffusion equation." Journal of Inverse and Ill-posed Problems, vol. 12, no. 3, 2004, pp. 243-256.
Kilbas, A. A., Srivastava, H. M., Trujillo, J. J. Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006.
Samko, S. G., Kilbas, A. A., Marichev, O. I. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, 1993.
Metzler, R., Klafter, J. "The random walk's guide to anomalous diffusion: a fractional dynamics approach." Physics Reports, vol. 339, no. 1, 2000, pp. 1-77.
Mainardi, F. Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College Press, 2010.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
