International Online Seminar on Mathematics and Its Applications

Saturday 23 May 2026, 00:00 → 23:20 UTC

Sultan Moulay Slimane

Manal Elzain Mohamed Abdalla (King Khalid University, Saudi Arabia), Rachid BAHLOUL (Sultan Moulay Slimane University, Morocco)

The International Seminar on Mathematics and its Applications aims to exchange information and ideas between researchers and practitioners from around the world, providing a platform to showcase the latest research, exchange ideas, and promote multidisciplinary collaboration.

Starts May 23, 2026, 10:00 AM

Ends May 23, 2026, 11:20 PM

1 SOME PROPERTIES OF η-MADIAL ON d-ALGEBRA

This work presents the concept of η-medial, which is an additional medial generalization. Furthermore, the notions of η-endomorphism and η-derivation are introduced, and some important properties are given. Finally, the condition for injectivity is obtained.

Speaker: Prof. RACHID BAHLOUL (Bahloul Rachid)

2 (α, n)-LAPLACE TRANSFORM AND THEIR APPLICATIONS

In this paper, we extend the formulas of both the Laplace and
Sumudu transforms to the (α, n)-conformable fractional order, and we derive and analyze several fundamental properties related to these two transforms.

Speaker: Ms KHADIJA EL GOURMATI (Sultan Moulay Slimane University, Beni Mellal, Morocco.)

3 A Frational Extension of AdamW

Adaptive optimizers such as Adam and AdamW have transformed
large-scale machine learning, yet they share a common structural
weakness: their memory of past gradients decays exponentially, so
gradient information older than roughly $1/(1-\beta_{1})$ iterations
rapidly vanishes. In highly non-convex, noisy, or ill-conditioned
optimization landscapes, this short-memory mechanism may prevent the
optimizer from exploiting long-range trajectory structure. We
propose \emph{Adaptive Fractional AdamW} , a new
optimizer that replaces the raw stochastic gradient in AdamW's
moment estimates with a normalized fractional long-memory
correction built on the Gr\"{u}nwald--Letnikov (G--L) operator.
Unlike existing fractional optimizers that fix the fractional
order $\alpha$ prior to training, FAAdamW continuously adapts
$\alpha_t$ based on the current gradient norm: when gradients are
large and informative the method behaves similarly to AdamW; when
gradients are small or noisy it increases its effective memory
depth automatically. We prove that FAAdamW reduces exactly to
standard AdamW when the memory length $K=0$, establish a
norm-boundedness lemma for the fractional correction, derive a
per-step stability bound, and provide a conditional
stationary-point convergence result under standard non-convex
stochastic assumptions. We also present an
approximate-reasoning interpretation of the correction as a
convex combination of gradient evidence governed by a power-law
credibility kernel, connecting the method to belief-function and
possibility-theory frameworks. Experiments on five analytical
benchmarks with stochastic noise, accompanied by ablation and
sensitivity studies, demonstrate that FAAdamW is competitive
with AdamW and other baselines, while providing improved stability
and reduced variance in several noisy, ill-conditioned, and
multimodal settings.

Speaker: Mr Houssam Rachad (Sultan Moulay Slimane University)

4 Analysis of a Diffusive Epidemic Model (SIR) with Crowley–Martin Incidence and Holling Type III Treatment in a Heterogeneous Environment

We study a reaction–diffusion SIR model that incorporates nonlinear infection and treatment effects.
We prove that the system is well posed by establishing the global existence of positive
solutions and deriving uniform bounds. Using variational arguments, we formulate the basic reproduction number R0 and analyze its threshold properties. In particular, we study the local and global stability of the disease-free equilibrium (DFE). Numerical simulations illustrate and support the analytical results, highlighting how diffusion interacts
with nonlinear incidence and saturating treatment in epidemic dynamics.

Speaker: Mr Oualid Bahouh (Faculty of Sciences and Techniques, Beni Mellal)

5 Higher-order conformable derivatives and their applications

After presenting some results and introducing a new definition of the higher-order conformable derivative, we discuss how these findings relate to a novel idea: The higher-order conformable Laplace
transform and the higher-order conformable Sumudu transform.

Speaker: Prof. Mohammed Bouziani (Center for Educational Orientation and Planning (COPE), BP 6222, Avenue Zaytoune, Hay Ryad, Rabat, Morocco.)

6 Generalization of derivations on lattices

Over the course of its development, the theory of binary operations
has become a foundational component of algebraic structures, providing a rigorous framework for the formulation and analysis of abstract algebraic structures and playing a central role in lattice theory and its numerous applications, where many fundamental notions and properties, including the very definition of a lattice, can be characterized and examined effectively in terms of appropriate binary operations.
In this study, we investigate the structural development of generalized γ-derivations on distributive lattices, where γ denotes a lattice homomorphism. We establish the following characterization: let η be a mapping from a distributive lattice to itself.
Then η is a generalized γ-derivation and a joinitive mapping if and only if η is a lattice homomorphism. Utilizing this homomorphic framework, we further analyze and derive several fundamental properties and salient characteristics of generalized γ-derivations. From an applications perspective, lattice structures play a central role in various domains, including information theory, information retrieval, and access control systems. Durfee employed techniques from the geometry of numbers to
address a range of cryptanalytic problems. Moreover, several public-key cryptosystems have been subjected to cryptanalysis via algebraic methods, with key results obtained through tools originating in the theory of integer lattices.

Speaker: Prof. Faiza Shujat (Taibah University, Madinah, Saudi Arabia)

7 On $d$-set derivative

The concept of new d-set derivatives resulting from certain algebraic operations (a law) was introduced. From this concept, a set of results and their applications were derived.

Speaker: Prof. Rania Saadeh (Al-Balqa Applied University, Jordan)

8 Linear Operators and Fractional Calculus in Banach Spaces Applications to Integral and Control Systems in Biomathematics

In recent years, the study of linear operators and fractional calculus in Banach spaces has gained significant attention due to its fundamental importance in both pure and applied mathematics. Banach spaces, as complete normed vector spaces, provide a general and powerful framework for analyzing a wide variety of problems, particularly those involving infinite-dimensional systems that frequently arise in functional analysis and mathematical modeling.
Linear operators are essential tools in this context, as they allow mathematicians to describe transformations between spaces and to investigate the structural and functional properties of mathematical systems. Their applications extend to solving differential and integral equations, which are central to many scientific and engineering disciplines. On the other hand, fractional calculus generalizes classical calculus by introducing derivatives and integrals of non-integer order. This extension has proven to be highly effective in modeling systems with memory, hereditary characteristics, and non-local behavior.
The integration of linear operator theory with fractional calculus offers a rich and flexible approach to studying complex systems, particularly in the field of biomathematics. Many biological processes, such as population dynamics, neural responses, and the spread of infectious diseases, exhibit behaviors that cannot be accurately captured using traditional integer-order models. Fractional models provide a more realistic description of these phenomena.
This research aims to investigate the theoretical foundations of linear operators and fractional calculus in Banach spaces and to explore their applications in integral equations and control systems within biomathematics. The study seeks to highlight the effectiveness of these mathematical tools in analyzing and solving real-world problems.

Speaker: Prof. Manal Elzain Mohamed Abdalla (King Khalid University, Saudi Arabia)

9 Small-Jump Approximation for Infinite-Intensity L´evy Processes

We investigate L´evy processes with infinite jump intensity and study the approximation of compensated small jumps by a suitably scaled continuous stochastic process.
We investigate the theoretical properties of small-jump approximations and study their convergence behavior in the framework of Lévy-driven stochastic models.

Speaker: Prof. Driss BOUGGAR (Hassan II University of Casablanca, Morocco.)