报告题目：Memory, Stability, and Geometric Evolution: New Results in Fractional Calculus, Trinition, and Mvog Theory

报告人：Abdon Atangana，南非自由州大学

报告时间：2026年9月24日（周四）14:00-16:00

报告地点：20-306；腾讯会议150- 452-742

报告摘要：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.                                                  

报告人简介：Abdon Atangana 是南非自由州大学应用数学教授、国际知名数学家，发表论文600余篇、专著十余部。他创立基于Mittag-Leffler核的分数阶微积分、分形-分数阶与分段微积分，提出Trinition与Aggregates理论，并在流行病建模中首创“强度数”概念。已培养博士15名、硕士25名、博士后10名。现任非洲工业与应用数学学会主席，获TWAS数学奖、联合国教科文组织Al Fozan奖，入选全球高被引学者前1%及前2%科学家。

邀请人：Yekini Shehu