This study introduces a novel linear operator incorporating both the Mittag-Leffler function and Lambert series to establish a new subclass of analytic functions denoted as . We first obtain sufficient conditions for functions to be members of . Consequently, we examine key properties including extreme points, coefficient constraints, and the radii of Univalency and starlikeness for functions in this subclass. In addition, by the means of Robin's inequalities, we provide some coefficients' lower bounds when applicable.

The main purpose of this manuscript is to prove some new fixed point theorems for a pair of multi dominated operators involving simulation function that satisfy a novel extension of Aydi-Lolo-Piri-Rasham type locally contractions in the setting of complete partial b-metric spaces. Also new results for multi-ordered dominated mappings and multi-graph dominated mappings are established on a closed ball in such spaces. To back up our findings, we give non-trivial illustrative examples for multi fixed points in partial b-metric spaces. Applications to the system of nonlinear Volterra type integral equations and fractional differential equations are given to show the novelty of our new results. Our hypothesis will be critical to the theory of fixed points. Our findings can be expanded and improved in various ways by employing multiple sorts of mappings in partial b-metric spaces with applications.

This paper investigates the nonlinear coupled Jaulent-Miodek (JM) and Whitham-Broer-Kaup (WBK) equations through the lens of fractional calculus, employing the Mohand Variational Iteration Method (MVIM) and q-Homotopy Mohand Transform Method (q-HMTM). These equations, pivotal in describing nonlinear wave phenomena and fluid dynamics, are studied in their fractional-order forms using the Caputo operator to extend traditional models. The proposed methods efficiently yield analytical and approximate solutions, showcasing their reliability and accuracy. The solutions derived are presented through numerical simulations and graphical depictions, revealing the intricate dependence of system behavior on fractional-order parameters. This sensitivity provides a mechanism for tuning physical phenomena modeled by JM and WBK equations, offering valuable insights into wave propagation, fluid dynamics, and other nonlinear coupled systems. The study establishes the efficacy of q-HMTM and MVIM in handling complex fractional-order systems, underlining their potential for broader applications in science and engineering. By bridging classical and fractional models, this work contributes to the ongoing development of advanced mathematical tools for analyzing nonlinear phenomena.

This study employs a novel approach to derive both approximate series and exact solutions to the fractional Black-Scholes model, utilizing the Elzaki transform and residual functions. This method is called the Elzaki Residual Method (ERM). By applying the basic limit principle at zero, the ERM demonstrates a superior ability to determine the coefficients of terms in the fractional power series, whereas other well-known methods such as the Adomian decomposition method, the variational iteration method, and the Homotopy perturbation method require integration, and the residual power series method relies on differentiation, both of which are challenging in fractional contexts. Moreover, the ERM outperforms series solution techniques that rely on Adomian and He’s polynomials for solving nonlinear problems, as it eliminates the need for such polynomials. To verify the reliability of our approach, we perform recurrence and absolute error analyses. Additionally, comparative assessments with the projected method, the Adomian method, and the Aboodh decomposition method demonstrate strong agreement. Finally, graphical illustrations further confirm the accuracy of our solutions. Therefore, the ERM can serve as a valuable alternative for solving both linear and nonlinear fractional systems. Maple software is used to calculate the numerical and symbolic quantities in the paper.

In this study, we developed a machine learning scheme to predict the occurrence of Second Primary Esophageal Squamous cell Carcinoma (SPESC) among patients with primary Head and Neck Cancer (HNC). This study retrospectively collected 2,863 records of patients with HNC, including 65 cases of SPESC. Data on 19 risk factors for SPESC were analyzed from the aforementioned records to identify significant risk factors and protective factors for SPESC. On the basis of gain ratios, the following significant risk factors were identified for the occurrence of SPESC in patients with HNC: age at HNC diagnosis < 65 years, tumor grade/differentiation > 2, smoking behavior, drinking behavior, and existence of a tumor depth measurement in the pathology report. The only significant protective factor for SPESC was Body Mass Index (BMI) ≥ 24. Data on the aforementioned factors were integrated into seven machine learning algorithms to predict the occurrence of SPESC: C4.5, C5.0, support vector machine, random forest, Classification and Regression Trees (CART), linear dynamic analysis, and logistic regression. Among these seven algorithms, CART exhibited the largest area under the receiver operating characteristic curve (0.9240); the highest accuracy (0.8678), recall rate (0.8573), F1 score (0.8871), and Matthews correlation coefficient (0.7305); and the lowest false positive rate (0.1990) for SPESC detection. Thus, CART was selected as the machine learning algorithm of the proposed model. The highest model accuracy of 88.0% was achieved under the following candidate factor conditions: drinking behavior: yes, age atdiagnosis: < 65 years, smoking behavior: yes, surgery: no, tumor size: ≤ 4 cm, BMI: < 24, radiotherapy: yes; and tumorgrade/differentiation: > 2. Overall, the developed prediction scheme enables the early and accurate detection of SPESCamong patients with HNC, thus improving patient outcomes and ensuring that patients with a low risk of developingSPESC do not need to undergo unnecessary invasive procedures.

Quantum computing threatens mainstream cryptosystems that rely on integer factorization and discrete-logarithm hardness assumptions. Although Post-Quantum Cryptography (PQC) and biometric authentication have each progressed rapidly, few solutions fuse their respective advantages. We present an AI-enhanced post-quantum two-tier authentication framework that unifies cryptographic robustness with adaptive, behaviour-based biometrics. Tier 1 uses conventional factors-passwords and static biometrics-to establish a baseline identity. Tier 2 then acquires dynamic emotional cues from facial expressions, speech prosody and physiological signals, which are continuously analysed by deep-learning models. The resulting emotion signatures are bound to the credential stream via a lattice-based chameleon hash and signed with the CRYSTALS-Dilithium scheme, yielding strong resistance to spoofing, coercion and quantum adversaries. Simulation results show a True Acceptance Rate of 95.7% and a False Acceptance Rate of 2.1% under targeted adversarial attacks. These findings demonstrate that coupling emotion-aware AI biometrics with PQC primitives can deliver adaptive, quantum-resilient authentication for next-generation digital infrastructure.

This study addresses a nonlinear 2D reaction-diffusion system governed by variable-order fractal fractional derivatives in both the Caputo and Atangana-Baleanu Caputo (ABC) senses. These derivatives are characterized by non-singular kernels involving Mittag-Leffler functions, capturing memory and hereditary effects in complex media. To obtain numerical solutions, a novel Non-standard Weighted average Finite Difference Method (NWFDM) is developed and implemented. This approach allows flexibility in temporal and spatial discretization while accommodating the variable fractional and fractal orders. A comprehensive analysis of stability using a von Neumann-type method and detailed error estimates is provided for both fractional formulations. Numerical simulations confirm the stability and accuracy of the proposed schemes, revealing the distinct impact of fractional parameters on system dynamics. The proposed methods exhibit superior performance compared to traditional schemes, particularly in capturing anomalous diffusion behavior in nonlinear environments. This study investigates a nonlinear 2D reaction-diffusion system incorporating variable-order fractal.

Hawkes processes are stochastic point processes with self-exciting behavior, where the occurrence of an event increases the probability of subsequent events. In this paper, we provide a concise yet comprehensive introduction to Hawkes processes, focused on applications. We then employ marked Hawkes processes to model the occurrences of transactions in European Union Allowances (EUA) futures. The models are trained using an innovative and efficient Maximum Likelihood Estimation (MLE) implementation, that leverages PyTorch library to parallelize computations and exploit automatic differentiation. We evaluate and compare different excitation functions using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Quantile-Quantile (Q-Q) plots based on the Random Time Change theorem. Additionally, we analyze the distribution of the calibrated parameters across different trading hours, finding the consistent relationship α = 3√(β2), to our knowledge never described before, between the self-exciting intensity parameter α and the decay parameter β . Furthermore, we identify two clusters: one characterized by transactions with a strong self-exciting effect, but that decays very quickly, and another with a less intense effect, that persists over longer time. Using logistic regression, we analyze the characteristics of the clusters and provide possible interpretations. We consider Hawkes processes very promising yet underutilized techniques for studying financial markets, and we believe this work can encourage researchers and practitioners to dive further into these models.

In this study numerical solutions for the compressible fluid flow around obstacles, based on a meshless method with Radial Basis Functions (RBFs) are presented. The numerical solutions are obtained by a hybrid method that uses the first step of the boundary element method, namely a singular boundary integral equation, which is an equivalent mathematical model for the problem of the compressible fluid around an obstacle, and then a meshless method based on RBFs for solving this singular boundary integral equation. Two types of RBFs are used, namely the Multiquadric RBFs and Gauss-type RBFs. An analytical check is made in order to study the numerical solutions' accuracy. Using computer simulations, we compare our results with an analytical solution available for a specific case. We examine how different parameters used to obtain the numerical solutions affect their accuracy, and we compare these numerical solutions to determine which RBF is most suitable for this scenario. We also note that the shape parameters of RBFs have a great influence on numerical solutions accuracy and, through simulations, optimal values are found. For evaluating the integrals of singular kernels which appear, the truncation method is applied. The influence of the parameter used to evaluate these integrals is also highlighted in the paper.

This paper reveals a nonlinear mathematical Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation in a biological system. This model has much importance in population genetics as well as nematic liquid crystals, explaining the reaction-diffusion system through traveling waves in population genetics as well as pattern formation in bi-stable systems. We use a fractional derivative to improve accuracy as well as understand the dynamics of the model. By utilizing the modified simplest equation method, we investigate the distinct kinds of exact wave solutions involving trigonometric, hyperbolic, and rational functions. To obtain and verify the solutions, we use the Mathematica software. We demonstrate the obtained solutions through 2-D, 3-D, and contour plots with the use of the Mathematica tool. The main contribution of this paper is to analyze the qualitative analyses, including stability analysis, modulation instability, and asymptotic analysis. At the end, the gained solutions are fruitful in different areas, like ecology, gene mutation, combustion theory, phase transition, and many others.