INVERSE PROBLEMS FOR GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL-ORDER DIFFERENTIAL OPERATORS

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.