This special issue on “Advances in Analysis, Algebra and Applied Mathematics” brings together contemporary research contributions addressing emerging challenges and opportunities in modern mathematics. It places particular emphasis on areas such as thermoelasticity, optimization, fractional calculus, summability theory, fixed point theory, and special functions, highlighting their theoretical advancements as well as their practical relevance to sustainable development. The volume focuses on innovative methodologies and interdisciplinary approaches, including the integration of fractional integral operators with special functions, the application of summability techniques, and the formulation of novel hybrid iterative schemes in fixed point theory. In addition, it presents significant generalizations of classical fixed point results and explores analytical frameworks relevant to thermoelastic models and optimization problems. Through these diverse contributions, the issue aims to highlight the role of advanced mathematical tools in addressing real-world scientific and engineering challenges.