Memory, Stability, and Geometric Evolution: New Results in Fractional Calculus, Trinition, and Mvog Theory（Abdon Atangana, University of the Free State, South Africa）

Speaker: Abdon Atangana, University of the Free State, South Africa

Time: 14:00–16:00, Thursday, 24 September 2026

Venue (In-person): Room 20-306

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Abstract: How can mathematics describe systems that retain memory, exhibit different dynamical responses, and evolve through deformation and reproduction? This lecture presents four complementary developments addressing these questions, connecting fractional analysis, spectral characterisation of dynamics, deformable geometry, and generational construction.

The first part presents recent results on the inversion of Caputo-type fractional derivatives through the Atangana integral. Attention is given to admissible function spaces, classical initial conditions, and fractional boundary traces. The resulting composition identities clarify the conditions under which a fundamental theorem of fractional calculus holds and identify the boundary information required for consistent reconstruction. The second part introduces the Atangana Strength Number as a dimensionless spectral indicator for characterising damping and distinguishing oscillatory from non-oscillatory local dynamics under appropriate stability assumptions.

The third part develops the Trinition framework, in which a deformation parameter connects algebraic relations with geometric structure. We examine how this parameter influences norms, anisotropy, and geometric degeneration, and discuss extensions involving constant, variable, and stochastic deformation. This provides a setting for investigating systems whose geometry forms part of their mathematical evolution.

The final part introduces Mvog theory as an axiomatic framework for reproductive geometry. Beginning with a founding object, called Tara, geometric structures develop through successive generations of offspring, with lineage, attachment, and connectivity explicitly represented. The discussion examines how these principles extend geometric construction beyond exact self-similarity and support the description of connected and disconnected evolving structures. Selected theoretical results and visual examples illustrate the interaction between reproductive rules and Trinition geometry.

The lecture brings these developments into a common research perspective: describing temporal memory, dynamical response, geometric deformation, and reproductive growth through explicit mathematical structures.

Speaker Bio:  Abdon Atangana is a Professor of Applied Mathematics at the University of the Free State, South Africa, and an internationally renowned mathematician. He currently serves as President of the African Society for Industrial and Applied Mathematics (ASIAM), and has received the TWAS Prize in Mathematics and the UNESCO Al Fozan Prize. He has been listed among the world's top 1% highly cited researchers and the top 2% of scientists globally.

Host: Yekini Shehu