International Online Seminar on Mathematics and Its Applications

Saturday 23 May 2026, 00:00 → 23:50 UTC

King Khalid University, Saudi Arabia. Sultan Moulay Slimane University, Morocco. Sorbonne University, France. (Manal Elzain Mohamed Abdalla, Rachid Bahloul, Svetlin G.Georgiev)

Manal Elzain Mohamed Abdalla (King Khalid University, Saudi Arabia), Rachid BAHLOUL (Laboratory LIMATI. Sultan Moulay Slimane University, Morocco), Svetlin G.Georgiev (Sorbonne University, Paris, France)

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 Chair

Speaker: Prof. RACHID BAHLOUL (Bahloul Rachid)

2 Coupled Nonlocal Boundary Value Problems for Fractional Integro-Differential Langevin System via Variable Coefficient

In this paper, we aim to study a new coupled system of nonlinear
fractional integro-differential Langevin equations with coupled multipoint
boundary conditions. The existence and uniqueness of solutions are investigated by using Banach’s and Krasnoselskii’s fixed-point theorems. The Ulam–Hyers stability of the mentioned equation is provided by applying
the classical technique of functional analysis. Two examples are presented
to verify our analysis.

Speakers: Prof. Kamal Ait Touchent (Abdelmalek Essaadi university Tanger morocco), Prof. Karim Guida (Abdelmalek Essaadi university Tangier morocco), Prof. Lahcen Ibnelazyz (Abdelmalek Essaadi university Tangier morocco)

3 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)

4 Modeling and Analysis of a Dual Epidemic Process under Deterministic and Stochastic Frameworks

This talk introduces a novel epidemic model that combines two distinct transmission mechanisms (SIS and SIR) to capture the simultaneous spread of two infectious diseases within a population. In the deterministic setting, we establish the existence and uniqueness of positive solutions and prove the local and global stability of the disease-free equilibrium. In the stochastic framework, we investigate the role of random perturbations and show that, depending on parameter conditions, the diseases may either go extinct or persist in the mean. Numerical simulations support the theoretical findings. This study highlights the relevance of considering multiple infections and environmental fluctuations in epidemic modeling, offering insights into the dynamics of coexisting diseases.

Speaker: Prof. Aziz Laaribi (Sultan Moulay Slimane University)

5 (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.)

6 Global convergence for a class of nonquasimonotone epidemiological models with delay

The new monotone dynamical theory is applied to a class of nonquasimonotone epidemic models with delay in this paper. Sufficient conditions for global convergence are derived.
Next, we study an SIS epidemic model with an exponential demographic structure and disease-related deaths and delays that coincide with the duration of the infection. Sufficient conditions for local and global stability for both free and endemic equilibrium are shown, as well as numerical simulations of each result. Our findings show the effectiveness of the monotone dynamical systems approach in epidemiological studies.

Speakers: Prof. Jaafar El Karkri (2Laboratory LERMA, Mohammadia School of Engineering, Mohammed V University), Prof. Kamal Ait Touchent (Laboratory 4 of Mathematics and Applications, Abdelmalek Essaadi University, Tangier, Morocco)

7 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.)

8 A two-step fractional kinetic model of a thermal explosion in class A geometries

In this paper, we present a fractional model to study the heat transfer
during the combustion of reactive materials on some class A geometries.
A detailed chemistry model, which accounts for the initiation and termination
steps with a temperature-dependent pre-exponential factor, was
considered to describe the combustion of reactive materials. We numerically solve the mathematical model using a finite difference method based on the L1 formula, which allowed us to examine the transient heat behavior by exploring the effects of the kinetic parameters embedded in
the governing fractional partial differential equation. Our results indicate that the reaction order reduces the exothermic chemical reaction, while the reaction rate accelerates the combustion process.

Speaker: Prof. M Er-Riani1 (Abdelmalek Essaadi University,)

9 INTRINSIC METRICS AND GEOMETRY OF DIRICHLET FORMS

We present a general conception of intrinsic metrics and study some of their properties. We provide general regular Dirichlet forms. Given a regular, strongly local Dirichlet form ℇ, the local doubling and local Poincaré inequalities are satisfied; we obtain that the intrinsic differential and distance structures of ℇ coincide.
This topic focuses on the extraction of an "intrinsic metric" from an abstract energy form, enabling the definition of distances and geometry on spaces that may lack a smooth differential structure (such as fractals or general metric measure spaces). The objective is to understand how "energy" dictates the topology and geometric properties of the space.

Speaker: Prof. HANANA ELNAGE MOBARK (King Khalid University, Saudi Arabia)

10 L-Dunford-Pettis property in Banach spaces

We introduce and study the concept of L-Dunford-Pettis sets and the L-Dunford-Pettis property in Banach spaces. Next, we give a characterization of the L-Dunford-Pettis property with respect to some well-known geometric
properties of Banach spaces. Finally, some complementability of operators on Banach spaces with the L-Dunford-Pettis property is also investigated.

Speakers: Prof. Abderrahman Retbi (Sultan Moulay Slimane University), Prof. Bouazza El Wahbi (Faculty of Sciences, Kenitra, Ibn Tofail University)

11 ABOODH RESIDUAL POWER SERIES METHOD FOR SOLVING LINEAR NEUTRAL FRACTIONAL PANTOGRAPH EQUATIONS

In the current work, we suggest a better representation of the Aboodh residual power series method of solving the linear neutral fractional pantograph equations. Among other methods of analysis, the current framework introduces a methodical algorithmic process that allows managing the linear case in a systematic manner. The resulting formula offers solutions in the form of convergent chains of infinite representations that are too fast to converge and numerically stable and incredibly accurate approximations. Special attention is given to the convergence pattern and the accuracy of the obtained approximations in the case of the exact analytical solutions. To further confirm the strength and usability of the suggested method, a number of exemplary numerical examples are given. These illustrations point to the efficiency of the method and prove its high level of convergence rate and simplicity of the computation. Python was used to perform all the simulations and numerical calculations to make them reproducible and provide accuracy in computations.

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

12 Monogenity of pure number fields: application to the existence of canonical number systems

Let m be a non-zero rational integer with m ̸= ±1, and consider
the pure number field K = Q( n
√
m), n ≥ 3.
Most published works on the monogenity of pure number fields
focus mainly on the case where m is square-free. For every positive
integer n ≥ 4, the monogenity of number fields of degree n is not yet
completely characterized. For instance, the monogenity of the pure
quartic field Q( 4
√
m) remains open, even under the assumption that m
is square-free.
In this talk, we present new results on the monogenity of pure number
fields K, without assuming that m is square-free. Our approach is
based on a classical theorem of Ore on the decomposition of prime ideals
in number fields, together with the use of Newton polygons. This
technique will be briefly discussed.
As an application, we provide several examples related to canonical
number systems (CNS). In particular, we show that our results extend
or partially complete several known results in the literature.

Speaker: Prof. Hamid ben yakkou (Sultan Moulay Slimane University)

13 Numerical and Theoretical Analysis of Time-Fractional Variational Inequalities with Applications to Frictional Contact

In this paper, we study a quasistatic frictional contact problem describing the interaction between a
thermo-viscoelastic body and a thermally conductive foundation. The mechanical response of the material
is modeled by a fractional Kelvin–Voigt constitutive relation, while the thermal behavior is governed by a
time-fractional evolution equation for the temperature field. The contact conditions are formulated
through the Signorini unilateral condition together with a Coulomb dry friction law.
A variational framework for the coupled problem is established, and the existence of a weak solution is
proved using techniques from monotone operator theory, the Galerkin approximation method, properties of the Caputo fractional derivative, and the Banach fixed-point theorem.
Finally, numerical experiments are presented to validate the proposed model and to demonstrate the stability, accuracy, and effectiveness of the developed computational approach.
Finally, numerical experiments are presented to validate the proposed model and to demonstrate the stability, accuracy, and effectiveness of the developed computational approach.

Speaker: Prof. Mustapha Bouallala (Polydisciplinary Faculty of Safi)

14 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)

15 Higher-order conformable Operational Analysis: Properties and Intergal Transformation.

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.)

16 Parabolic Volterra Equations with Memory: Analytic Resolvents and Maximal Regularity

In this seminar, we focus on a class of parabolic Volterra equations in Banach spaces. We
explain why the classical semigroup approach is not always sufficient and how resolvent families offer a more
appropriate tool for studying these equations. The talk will highlight the role of parabolicity assumptions on
the memory kernel and the linear operator, and show how these conditions lead to the existence of analytic
resolvents.
We will also discuss the regularizing properties of analytic resolvent families and their connection with maximal
regularity. The aim is to present the main ideas in a clear and accessible way, while emphasizing the
importance of these methods in the analysis of integro-differential evolution equations with memory.

Speaker: Ms Khadija Zahidi (Sultan Moulay Slimane University)

17 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)

18 Construction of Resolvent Families via the Subordination Principle

In this work, we investigate convolution-type Volterra integral equations through the subordination principle. This approach enables the construction of new resolvent families from already known ones. We first discuss several important classes of scalar kernels and present some of their fundamental properties. We then establish a representation formula for the subordinated resolvent family in terms of the original resolvent. The obtained results provide a useful framework for the analysis of Volterra equations and their associated resolvent families.

Speaker: Mr Rachid GUIRHIR (Sultan Moulay Slimane University)

19 Fixed Point Theory for Contractive Mappings in G- Metric Spaces.

This study develops a systematic investigation of fixed-point theory for contractive mappings within the framework of complete G-metric spaces, we highlight possible applications of metric fixed-point theory across diverse scientific and engineering contexts, such as control theory, population dynamics, signal processing, and wavelet analysis. These applications demonstrate the broad potential of fixed-point methods in solving real-world problems, we focus on mappings defined on complete G-metric spaces, presenting convergence results and characterizing conditions under which mappings admit fixed points. Particular attention is given to the continuity properties of such mappings at fixed points and the uniqueness of solutions under contractive assumptions; finally, we extend the analysis to contractive mappings in G-metric spaces, establishing existence and uniqueness results under various contractive conditions. These results are further generalized to fuzzy metric spaces, cone metric spaces, generalized metric spaces, and complex-valued metric spaces, as well as to weakly compatible mappings under integral-type contractive conditions. Coincidence point theorems for sequentially continuous mappings are also addressed. The findings not only unify and extend several known fixed-point results but also provide new tools for the study of nonlinear boundary value problems and elliptic systems with singularities or discontinuities. Overall, this study underlines the central role of fixed-point theory as a bridge between abstract analysis and applied mathematical models.

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

20 Existence and uniqueness of a positive, compactly almost automorphic solution.

In this paper we consider the logistic equation with diffusion under the assumption that its coefficients are almost automorphic. We establish sufficient conditions for the existence and uniqueness of a positive, compactly almost automorphic solution on R. Moreover, we prove that this solution is spatially homogeneous and attracts all positive solutions.

Speaker: Dr Youssef Lakdim (Faculté des Sciences Semlalia de Marrakech)