Annals of Mathematics and Computer Science

New Approach for Analysis of Solution of Certain Fractional Sum-Difference Equations

Yogesh Shirole — 2026-07-21

This paper investigates a class of nonlinear fractional sum–difference equations in a discrete setting. By converting the considered problem into an equivalent fractional summation equation, fixed point techniques are effectively applied to analyze the behavior of solutions. The existence of solutions is established through the Leray–Schauder alternative, whereas uniqueness is derived using a discrete form of Bihari’s inequality. The obtained results extend several existing works related to fractional discrete systems under suitable growth conditions. Moreover, the developed approach offers an efficient framework for studying nonlinear fractional dynamical models with memory effects arising in discrete fractional calculus.

Innovative Option Pricing Using the Conformable Black Scholes Model

Abdessamad AIT BRAHIM — 2026-07-21

Fractional calculus has become an important tool in financial modeling due to its ability to capture memory effects and anomalous diffusion observed in financial markets. In this paper, we develop a fractional extension of the classical Black–Scholes option pricing model using the conformable fractional derivative. Owing to its local nature and preservation of key properties of classical differentiation, the conformable derivative allows for an analytically tractable and arbitrage-free framework. We derive the conformable fractional Black–Scholes partial differential equation, obtain closed-form solutions for European options, and provide a financial interpretation of the fractional order parameter.

Markov and Hidden Markov Models for Genomic Sequence Classification

Ali Souleymane DABYE — 2026-07-21

The rapid growth of genomic data generated by high-throughput sequencing technologies has created significant challenges for statistical modeling and sequence classification. In this paper, we investigate genomic sequence classification using probabilistic and machine learning approaches based on Markov chains, Hidden Markov Models (HMMs), and Support Vector Machines (SVMs). Markov and Hidden Markov models are employed to capture local nucleotide dependencies and latent biological structures associated with coding and non-coding regions. Building upon these models, we introduce a hybrid HMM–SVM framework that combines generative likelihood-based features, hidden-state representations, and biologically interpretable compositional descriptors. Experimental results on genomic data demonstrate that the proposed hybrid approach substantially improves classification performance while maintaining biological interpretability.

Some Results on Symmetrized A H-Convexity

Jamal El-achky — 2026-07-21

The Hermite-Hadamard inequality is applied to several classes of functions in many fields of analysis. This inequality has become a powerful mathematical tool for researchers. The idea of convexity has undergone numerous generalizations and extensions in recent years. This study presents the concept of a symmetrized AH-convex function and proves Hermite-Hadamard type inequalities via symmetrized A H-convex function and symmetrized h-A H-convex function.

Risk Modeling on the BRVM

Vini Yves Bernadin LOYARA — 2026-07-21

Classical risk measurement models assume normality of returns and linear dependence, which systematically underestimates extreme losses in emerging markets. This paper evaluates two complementary approaches to model the risk of a portfolio of BRVM assets (SONATURG and BOA BF) over 2020–2023. The first uses copulas to capture tail dependence between assets. The second employs Markov chains to model market regime persistence. Results show that the Student's t-copula captures non-zero tail dependence (0.28) and the Markov chain reveals strong regime inertia (probability of staying in same regime above 0.85). Combining both approaches provides a more comprehensive view of risk for BRVM investors.

Adaptive Hybrid B-Spline PINN for Fractional Equations

Balaji Padhy — 2026-07-21

We propose a hybrid numerical framework combining a redefined quintic B-spline collocation method with a Physics-Informed Neural Network (PINN) correction layer for solving nonlinear space-time fractional advection-diffusion-reaction equations. The spatial fractional derivative is discretised via a shifted Grünwald–Letnikov approximation embedded in the B-spline basis, achieving high-order spatial accuracy. The temporal Caputo derivative is handled by an L2-1σ Crank–Nicolson scheme surpassing standard methods. A PINN residual corrector suppresses oscillations in high-Péclet-number regimes without mesh refinement. Adaptive time-stepping reduces computational cost by over 60%. Rigorous stability and convergence analysis are provided. Seven benchmark problems confirm the framework outperforms existing quintic B-spline, spectral, and PINN-only methods by one to two orders of magnitude.

Evaluating Zero-Day Generalisation in VANET Detection

Anthony Ibrahim — 2026-07-21

The rapid expansion of the Internet of Vehicles has introduced security vulnerabilities, requiring robust Intrusion Detection Systems. This study evaluates the generalisation capabilities of Random Forest, XGBoost, Naive Bayes, Logistic Regression and Extra Trees against zero-day vehicular attacks. Using the VeReMi NextGen dataset, the methodology separates known and unseen attacks using the Leave-One-Attack-Out strategy to simulate realistic, unseen threat scenarios. Results demonstrate that while Random Forest excels at identifying known threats, it suffers from overfitting, resulting in a low F1-score for zero-day attacks. Conversely, XGBoost and Extra Trees exhibit more consistent zero-day performance, suggesting improved robustness against novel vehicular attacks.

3D Navier-Stokes Equation with Multivalued Friction

Simon ZONGO — 2026-07-21

We prove the existence of weak solutions and their continuous dependence on the data for a three-dimensional incompressible Navier-Stokes system subject to multivalued friction boundary conditions, within a Hilbert space framework. Under suitable assumptions, a fixed point argument yields the existence of a solution to the associated perturbed stationary problem. Using nonlinear semigroup theory, we then establish the existence of a mild solution to the non-stationary problem and prove a contraction principle. Finally, by combining the Crandall-Liggett implicit discretization scheme with a priori estimates for the approximating mild solutions, we obtain weak solutions that depend continuously on the initial data.

Approximation on Fixed Point for F-Iterative Scheme

Vinod Kumar Sahu — 2026-07-21

In this paper, we study the approximation of fixed points of mappings satisfying the (η,θ)-condition in uniformly convex Banach spaces. Using the F-iterative scheme, we establish weak and strong convergence results under suitable assumptions. Our results extend and generalize several existing fixed point theorems, including those for Suzuki-type mappings. Finally, the applicability of the proposed (η,θ)-condition and the associated iterative scheme is demonstrated through an image restoration problem, supported by numerical experiments.

Quasilinear Elliptic Equations via Gradient-Form-Boundedness

Mykola Yaremenko — 2026-07-21

This paper studies the Dirichlet problem for quasilinear elliptic equations with singular coefficients, extending the classical Ladyzhenskaya-Ural'tseva theory. We replace the standard L-r-integrability condition (with r greater than n) with a more flexible p-gradient-form-boundedness assumption. Under this weakened hypothesis, we establish local and global a priori estimates, existence of weak solutions, and Holder continuity of bounded weak solutions. The results hold on arbitrary bounded open sets without boundary regularity requirements.