Assoc. Prof. Dr. Sultan Aldırmaz Çolak has established an influential research career in applied mathematics, with particular emphasis on fractional calculus, functional analysis, operator theory, q-calculus, inequalities, optimization techniques, and mathematical modeling. The work integrates both theoretical and applied perspectives, contributing to the development of new mathematical structures and analytical approaches. A strong research presence is visible in fractional differential equations, fractional inequalities, and variational principles, where innovative methodologies are applied to solve complex problems in pure and applied sciences. Contributions extend to fractional operators with general kernels, quantum calculus, approximation theory, fixed point theorems, and applications of conformable fractional derivatives, reflecting versatility in addressing modern mathematical challenges. Publications highlight advances in inequalities of Hermite–Hadamard type, generalizations of classical results, and connections between fractional calculus and convexity theory. Beyond core mathematics, research interests also include mathematical programming, optimization problems, and algorithmic approaches, establishing bridges with computer science and applied engineering. Engagement in international collaborations has broadened the reach of this research, demonstrated through joint works published in reputed journals across mathematical sciences. The scientific output emphasizes originality in both problem formulation and solution strategies, making significant contributions to ongoing discourse in advanced calculus and related domains. Focus areas like generalized convex functions, applications of Jensen’s inequality, integral transforms, and iterative methods for nonlinear operators position this work at the interface of analysis, computation, and modeling. Active participation in editorial roles and peer review further indicates a commitment to advancing the discipline. Overall, the research achievements of Assoc. Prof. Dr. Sultan Aldırmaz Çolak represent a consistent pursuit of mathematical innovation with practical relevance across interdisciplinary boundaries. 486 Citations 54 Documents 11