On 1 March 2026, at VNUHCM–University of Science (HCMUS), researcher Hoàng Văn Đại (2022 cohort, Mathematical Analysis) successfully defended a doctoral thesis entitled “Investigation of Several Non-local Problems Involving Fractional Derivatives”. The research was conducted under the academic supervision of Assoc.Prof. Nguyễn Huy Tuấn and Assoc.Prof. Bùi Lê Trọng Thanh.

During the presentation, the researcher elucidated three primary groups of problems within the field of partial differential equations: non-local problems with Riemann–Liouville derivatives; problems utilising modified Caputo derivatives; and fractional Rayleigh–Stokes equations featuring exponential nonlinear source terms. Built upon a systematically constructed theoretical framework, the thesis establishes conditions ensuring the existence, uniqueness, and stability of solutions, whilst further analysing ill-posed scenarios frequently arising in models with non-local elements.

To address specific challenges inherent in these problems, the research employs a versatile range of modern analytical tools, including the concept of mild solutions, fixed-point theorems, Sobolev embeddings, spectral analysis, and fundamental inequalities. Such an approach facilitates an extension of the scope of investigation for classes of equations with more complex structures than previously published results.

Notable contributions of the thesis include: establishing a theoretical framework for problems involving various forms of fractional derivatives; proposing methods to handle ill-posed problems via the concept of mild solutions; and providing supplementary research findings on fractional Rayleigh–Stokes equations with exponential nonlinear sources—a field hitherto seldom explored domestically. These results contribute to the refinement of the theoretical foundations for models characterised by memory effects and non-local interactions.

Regarding practical applications, the findings may assist in modelling physical and engineering phenomena such as anomalous diffusion, the motion of viscous fluids, heat transfer in specialised materials, and certain financial models. Furthermore, the thesis suggests potential for developing discretisation methods and numerical algorithms for simulation-based research in computational science. This work also serves as an advanced reference for teaching and future research directions in the field of fractional partial differential equations.

In addition to the achieved results, the researcher proposed future developments, such as extending the models to more complex nonlinear structures, considering alternative definitions of fractional derivatives, and constructing efficient numerical methods to optimise computational costs and enhance interdisciplinary applicability.

Concluding the session, the Examination Committee determined that the thesis satisfies all requirements for a doctoral degree under current regulations and unanimously approved the work. The thesis was judged to meet the required standards, possessing significant reference value for both specialist training and academic research.