Documents published in Scipedia

• Advanced Computational Study of Nonlinear Time-Fractional NewellWhitehead-Segel Equation with Caputo-Fabrizio Derivative Using B-Spline Techniques

  M. Shafique, M. Yaseeen, S. Trabelsi, M. Balti

  
  

  Abstract

  This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized using three B-splines-cubic, cubic trigonometric and extended cubic B-splines-while temporal discretization is handled by a finite difference scheme. The proposed schemes are rigorously analyzed for stability and convergence. Their performance is evaluated in terms of accuracy and computational efficiency. Numerical experiments confirm the effectiveness of these techniques in capturing the dynamics of the fractional NWS equation. Each B-spline variant demonstrates unique strengths, highlighting the flexibility of B-spline approaches for solving fractional differential equations with nonlocal, memory-dependent operators. These results affirm the reliability and robustness of B-spline-based methods for such problems, paving the way for future advancements in this area.OPEN ACCESS Received: 23/08/2025 Accepted: 08/12/2025 Published: 16/04/2026

  Abstract
  This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized [...]

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• Qualitative Analysis of Nonlinear Systems Involving Hadamard-Type Fractional Derivatives with Nonlocal Boundary Conditions and Stability Properties

  M. Manigandan, M. Awadalla, R. Shanthi, S. Trabelsi

  
  

  Abstract

  This paper establishes a comprehensive analysis of a coupled system of nonlinear Hadamard-type fractional differential equations subject to generalized nonlocal integral boundary conditions. The distinct logarithmic kernel of the Hadamard derivative makes this framework particularly suitable for modeling scale-invariant processes and ultraslow diffusion phenomena. The existence and uniqueness of solutions are rigorously investigated using fixed point theory: Banach’s contraction principle ensures uniqueness, while the Leray-Schauder nonlinear alternative guarantees existence under more general growth conditions. Furthermore, the system is proven to be Ulam-Hyers stable, ensuring that approximate solutions remain close to exact solutions, which is crucial for the robustness of the model in practical applications. The theoretical findings are effectively validated through two detailed numerical examples, demonstrating the applicability of the established results to different classes of nonlinearities.OPEN ACCESS Received: 22/08/2025 Accepted: 03/11/2025 Published: 23/01/2026

  Abstract
  This paper establishes a comprehensive analysis of a coupled system of nonlinear Hadamard-type fractional differential equations subject to generalized nonlocal integral boundary [...]

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• Construction and Orthogonality of Fractional Laguerre Functions via the Caputo Derivative

  K. Abuasbeh, M. Awadalla, A. Sharif, M. Balti

  
  

  Abstract

  This paper presents a rigorous framework for generalizing Laguerre polynomials to the fractional domain using the Caputo derivative. We solve the resulting fractional Laguerre differential equation via the power series method, deriving an explicit formfor the fractional Laguerre functions. A key contribution is the identification of a novel weight function, wα(x) = x−(2α−1)e−x, which is essential to prove the orthogonality of these functions over the interval [0,∞). Comprehensive numerical validation is provided, confirming the theoretical orthogonality across a wide range of fractional orders α and demonstrating a clean reduction to the classical polynomials when α = 2. An analysis of computational feasibility confirms the practical applicability of these functions for solving fractional differential equations and other applied problems.

  Abstract
  This paper presents a rigorous framework for generalizing Laguerre polynomials to the fractional domain using the Caputo derivative. We solve the resulting fractional Laguerre [...]

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• Dynamic and Control in a Three-Variable Chemical Reaction Model

  M. Martinez, F. Chavarette

  
  

  Abstract

  Chaotic behavior in nonlinear chemical systems presents significant challenges for stability and control, particularly in practical applications.This study investigates the suppression of chaos in a three-variable reaction system through an optimal linear feedback strategy, formulated via the solution of an algebraic Riccati equation.The proposed control approach effectively eliminates chaotic oscillations, guiding the system to equilibrium even under parameter uncertainties of up to 20%. Numerical simulations confirm that the control action maintains high robustness, ensuring convergence with minimal effort. The stabilization time for x1 remains close to 29 s across different tolerances, while x2 and x3 converge nearly instantly, demonstrating the rapid effectiveness of the method. Furthermore, the control signal stabilizes at a small positive value after a short transient, reinforcing the computational efficiency and practical feasibility of this approach. These findings demonstrate that optimal linear control techniques provide a reliable and theoretically sound framework for managing nonlinear chemical systems, offering an accessible solution for real-world applications in engineering and process optimization.

  Abstract
  Chaotic behavior in nonlinear chemical systems presents significant challenges for stability and control, particularly in practical applications.This study investigates the [...]

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• Coupled Thermal and Solutal Transport in Magnetic Nanofluids with Field-Dependent Viscosity in Porous Media: A Stability Perspective

  M. Arora, M. Sharma

  
  

  Abstract

  This study investigates the linear stability of double-diffusive convection in magnetic nanofluids (MNFs) within a horizontal porous medium, accounting for field–dependent viscosity (FDV). A modified Buongiorno– type model incorporates Brownian motion, thermophoresis, magnetophoresis, and Darcy resistance. The resulting eigenvalue problem is solved via a Chebyshev pseudospectral–QZ algorithm under rigid–rigid (RR), rigid–free (RF), and free–free (FF) boundary conditions for both water–based (Wb) and ester–based (Eb) MNFs. Results show that magnetic and solutal effects lower the critical Rayleigh number (Rac) from the classical Darcy–Bénard limit of ≈39.48 to as low as ≈23.8, indicating enhanced instability. In contrast, increasing the FDV coefficient (δ), Langevin parameter (αL), and nanoparticle concentration difference (�φ) raises Rac, stabilizing the system. Eb–MNFs exhibit consistently higher Rac values—by 15%–20% compared to Wb–MNFs, due to greater viscosity and lower thermal diffusivity. These findings clarify the interplay of magnetoviscous damping and solutal buoyancy, offering predictive insights for the design of magnetically tunable porous heat exchangers and thermal management systems.

  Abstract
  This study investigates the linear stability of double-diffusive convection in magnetic nanofluids (MNFs) within a horizontal porous medium, accounting for field–dependent [...]

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• Analysis of Airflow Velocity on Microdroplets Using Weibull StressStress Reliability Index under Unified Type-I Progressive Hybrid Data

  M. Nassar, R. Alotaibi, A. Elshahhat

  
  

  Abstract

  This work presents a novel and comprehensive inferential framework for analyzing the stress-strength reliability parameter,R= P(Y < X), where X and Y denote independent stress and strength variables, respectively, both modeled as Weibull-distributed with a shared shape parameter but distinct scale parameters. A key innovation of this study lies in its integration of the unified Type-I progressively hybrid censoring scheme, which simultaneously accommodates time constraints and partial failure information, conditions often encountered in real-world reliability testing. To estimate R, we propose and evaluate four distinct inferential strategies: two frequentist (maximum likelihood estimation and maximum spacings estimation) and two Bayesian, each tailored to either the likelihood or spacings-based posterior formulation. The Bayesian methods employ Monte Carlo sampling to compute both Bayes point estimates and credible intervals under informative priors, offering robustness in small-sample or heavily censored contexts. An extensive simulation study is conducted to systematically compare the estimators in terms of bias, efficiency, and interval coverage. To validate the practical applicability of our framework, we further analyze two real-world microdroplet datasets, revealing critical insights into stress-tolerance behavior under experimental constraints. This study not only advances methodological tools for reliability inference under hybrid censoring but also establishes a blueprint for combining classical and Bayesian paradigms in stress-strength modeling.OPEN ACCESS Received: 01/07/2025 Accepted: 02/09/2025 Published: 23/01/2026

  Abstract
  This work presents a novel and comprehensive inferential framework for analyzing the stress-strength reliability parameter,R= P(Y < X), where X and Y denote independent [...]

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• Analysis of Burr-XII Lifespan Using Adaptive Progressive Type-II Hybrid Binomial Censoring with Physical Modeling of Polyester and Carbon Fibers

  R. Alotaibi, H. Rezk, A. Elshahhat

  
  

  Abstract

  This study introduces advanced statistical methods, allowing for more efficient and accurate reliability testing of fibers such as polyester and carbon. Polyester ficbers are suitable for textiles and industrial use due to their wrinkle resistance and affordability, while carbon fibers offer superior strength, thermal stability, and corrosion resistance. To guarantee greater efficiency of inference methodologies and reduce overall testing time, the adaptive Type-II progressive hybrid censoring via binomial removals has gained popularity in reliability analysis and life-testing problems. The proposed scheme allows survival units to be removed at random stages according to a binomial law, thereby reducing experimental time while preserving statistical efficiency. When lifetimes are gathered using the suggested censoring technique, point and interval estimates of the unknown parameters of the Burr-XII model are obtained using both classical and Bayesian approaches. We obtain various Bayesian estimates using the squared loss function. Some numerical methods are employed to obtain the suggested estimators due to their complexity. The various Bayes estimates and related credible intervals are created using Markov chain Monte Carlo techniques. To assess estimator performance, extensive simulation studies are conducted, comparing bias, mean squared error, coverage probabilities, and interval lengths under varying censoring and removal settings. The simulation results confirm that the Bayesian framework, particularly with informative priors, provides more accurate and stable estimates than asymptotic likelihood-based methods. We examine two physics data sets representing polyester and carbon fibers to demonstrate the relevance of the suggested approaches in a real-world setting. These applications highlight the practical value of the proposed approach for material design, maintenance planning, and broader reliability engineering problems.OPEN ACCESS Received: 13/06/2025 Accepted: 12/09/2025 Published: 23/01/2026

  Abstract
  This study introduces advanced statistical methods, allowing for more efficient and accurate reliability testing of fibers such as polyester and carbon. Polyester ficbers [...]

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• On Nonlinear Monge-Ampère Equations and Their Symmetry Classifications

  Z. Izgi, Ö. Avit, D. Baleanu, M. Yousif, M. Alharthi, P. Mohammed

  
  

  Abstract

  The Monge-Ampère equation (MAE) plays a pivotal role across a broad spectrum of theoretical and applied sciences, with its solutions being essential for advancing various fields. This study explores all forms of the fully nonlinear MAE using Lie group transformations to reduce the equation into solvable forms. Analytical solutions are derived using ansatzbased methods, yielding novel and generalized results that enhance the existing body of knowledge. In particular, solutions for cases with diverse source functions and boundary conditions are obtained, addressing gaps in the literature. Stability of the solutions is studied through both analytical and numerical approaches. Comparisons with existing solutions demonstrate the efficiency and generality of the proposed methods. The results presented in this work are poised to impact numerous applications, providing a robust framework for further research on MAEs.OPEN ACCESS Received: 24/05/2025 Accepted: 07/08/2025 Published: 27/10/2025

  Abstract
  The Monge-Ampère equation (MAE) plays a pivotal role across a broad spectrum of theoretical and applied sciences, with its solutions being essential for advancing various [...]

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• Integration of Monte Carlo Simulation and Linear Programming in Multi-Product Multi-Stage Supply Chains: A Theoretical Framework for Decision-Making under Uncertainty

  K. Abuhasel

  
  

  Abstract

  This study outlines a hybrid Monte Carlo Simulation-Linear Programming framework to increase the level of operational efficiency of a multistage supply chain. This model is an integration of probabilistic simulation and deterministic optimization to take into account the effects of demand variability, lead-time variability, and capacity variability on profitability and the overall service delivery performance. The suggested framework is tested with the help of a multi-product, multi-stage supply chain case study that is implemented on the basis of a publicly available dataset containing around 9000 transactional records. Monte Carlo simulation generates random uncertainty scenarios, whereas linear programming finds the ideal decisions related to production, distribution, and inventory levels for each iteration. The results suggest that reducing the amount of demand variability and better capacity planning resulted in a good performance with an expected profit of $328,100.16, a profit variance of 3.72× 109, and a service level of 94.3%. The result of the sensitivity analysis shows that demand variability and lead times have a negative effect on profit, while optimal capacity planning enhances operational flexibility. The MCS-LP provides an advantage to the use of stochastic and deterministic methods for risk-aware decision making and has the potential to be computationally scalable and efficient for uncertaintydriven supply chain design. The general approach provides a decisionsupport tool for managers considering how to balance costs, risk, service quality, and uncertainty in ever-changing industrial contexts.OPEN ACCESS Received: 14/11/2025 Accepted: 13/01/2026 Published: 20/03/2026

  Abstract
  This study outlines a hybrid Monte Carlo Simulation-Linear Programming framework to increase the level of operational efficiency of a multistage supply chain. This model is [...]

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• AI-Driven Predictive Analytics for Demand Forecasting in Transportation Logistics to Enhance Supply Chain Agility

  K. Abuhasel

  
  

  Abstract

  The logistics and transportation sectors are struggling with major issues like demand variations, disruptions, and inefficiencies, which ultimately undermine the agility and efficiency of the entire supply chain. Most of the time, traditional forecasting models are not entirely accurate in response to life-changing factors like weather, traffic, and inventory levels. The present research intends to build an AI-powered predictive model that can seamlessly enhance not only demand forecasting and logistics but also by the integration of real-time data. The framework incorporates several Machine Learning (ML) models, which are Light GBM for demand forecasting, Random Forest for disruption prediction, Linear Regression for shipping cost estimation, and Support Vector Regression for delivery time deviation prediction. A thorough dataset containing historical demand, weather conditions, traffic, and stock levels was used for the model’s training and evaluation, and its performance was monitored using MAE, MSE, RMSE, and MAPE metrics. The findings indicate that the suggested framework is a lot better than the existing ones, with Light GBM getting the lowest MAE (0.056), MSE (0.005), RMSE (0.072), and MAPE (0.142). This means that the new system can predict much better than before, thus making it possible for the company to take the right decision at the right time and consequently improving the overall supply chain efficiency. The research paper reveals the future possibilities of AI-based solutions for optimising logistics operations and building supply chain resilience.OPEN ACCESS Received: 20/10/2025 Accepted: 25/12/2025 Published: 03/02/2026

  Abstract
  The logistics and transportation sectors are struggling with major issues like demand variations, disruptions, and inefficiencies, which ultimately undermine the agility and [...]

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