Fractional Calculus and Quantum Calculus

Fractional Calculus and Quantum Calculus presents a focused collection of contemporary research on fractional calculus, quantum (q-) calculus, and generalized calculus, highlighting recent theoretical developments and their emerging applications across mathematics, science, and engineering. The volume brings together contributions on analytical and computational methods for fractional differential and integro-differential equations, addressing fundamental topics such as existence, uniqueness, stability, controllability, and nonlocal and delay effects. It explores advances in quantum calculus through q-Sturm–Liouville theory and q-matrix generated sequence spaces, with emphasis on operator theory, summability, and geometric properties in functional analysis. The book further develops generalized fractional and nonlocal integral operators with novel kernels, broadening the mathematical framework for modelling complex systems. Additional chapters present recent progress in statistical and rough convergence within fuzzy normed spaces, fractional difference sequence spaces, and SUM integral transforms, providing powerful tools for convergence analysis and computational techniques. The inclusion of fractional-order gradient descent methods also demonstrates the growing impact of fractional calculus in machine learning, optimization, and data-driven computation. Overall, the book offers a concise yet rigorous resource for researchers in fractional and quantum calculus, functional analysis, numerical methods, and interdisciplinary applications involving memory, nonlocality, and discrete–continuous dynamics.