This study explores the application of the Adomian Decomposition Method (ADM), combined with the Laplace transform, to obtain approximate solutions of the time--fractional Wazwaz--Benjamin--Bona--Mahony (WBBM) equations. These equations, which describe wave phenomena in fluid dynamics within a fractional--time framework, present significant analytical challenges. By integrating the Laplace transform with ADM, a modified technique---referred to as the Laplace Transform Adomian Decomposition Method (LTADM)---is introduced. The time--fractional WBBM equations are solved using LTADM, and three--dimensional solution plots are generated for six different values of the fractional order \( \delta \)... More >

The underpinnings, usage, and capabilities of source code developed to simultaneously compute and display the temporal evolution of quantum-mechanical wavefunctions are described. This computation is done through direct numerical integration of Schrödinger's equation and is limited to one spatial dimension. The source code is freely downloadable for noncommercial, educational purposes. The Schrödinger equation's linearity in facilitating the computations along with important restrictions imposed by the algorithms employed are emphasized. Physical interpretations of the example systems treated are highlighted. Plenty of citations and footnotes are provided---both historical and pedagogical.... More >

In this paper, the concept of the bipolar spherical fuzzy set (BSFS) and its operations is developed. It is proposed as a generalization of fuzzy sets, bipolar fuzzy sets, picture fuzzy sets, and spherical fuzzy sets, allowing uncertain information to be handled more flexibly in the decision-making process. The key objective of this research paper is to introduce a new version of the spherical fuzzy set so called bipolar spherical fuzzy set (BSFS). The bipolar spherical fuzzy set is a new extension of spherical fuzzy sets and picture fuzzy sets. In bipolar spherical fuzzy sets, membership degrees are satisfying the condition \( 0 \leq (s^+)^2(x) + (i^+)^2(x) + (d^+)^2(x) \leq 1 \) and \( 0 \... More >

The initial mathematical model for rabies consists of six compartments representing the human and dog populations: $S_h, I_h, V_h, S_d, I_d, V_d$. To obtain a more realistic description of rabies transmission dynamics, we extend the model by introducing two additional human compartments: Exposed ($E_h$) and Recovered ($R_h$) individuals. The extended system therefore comprises eight compartments: $S_h, E_h, I_h, V_h, R_h, S_d, I_d, V_d$. This extension captures important differences in disease progression, treatment response, and transmission pathways. Within this framework, we examine the positivity and boundedness of solutions, derive the basic reproduction number ($R_0$), analyse the sens... More >

Previous research has focused on formulating cancer treatment strategies within a single-drug framework, which clearly fails to effectively address the practical needs of combination drug therapy in clinical settings. Therefore, this study develops a multi-drug cancer treatment model and conducts strategy design and simulation investigations under hypothetical patient-specific parameters for dual-drug regimens. Based on the previously proposed adaptive threshold strategy and several novel strategies integrating threshold-based and sequential administration patterns, and conducted a parameter search and optimization of upper/lower thresholds was performed to explore the performance improvemen... More >