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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.
Dr. Parthapratim Saha is Assistant Professor at the Sipajhar Coll., India. He is a doctoral scholar of Prof. Bipan Hazarika from Gauhati Univ.. His current research focuses on Harmonic analysis, integration theory, measure theory, function spaces, Fractional calculus, Quantum calculus. Dr. Saha has a bright academic career. He is a gold medalist in Mathematics at B.Sc level from Gauhati university and secured 1st class third position in M.Sc. in Mathematics from Gauhati University. He has academic experience of several years and has published and reviewed many research papers in reputed journals. Dr. Saha is an expert speaker in various national and International Conferences.
Dr. Hemanta Kalita is Assistant Professor, VIT Bhopal Univ., India. Dr. Hemanta Kalita is a Doctorate from Gauhati University under the guidance of Prof. Bipan Hazarika. He has an academic experience of 13 years and has worked at various levels up to Assistant Professor. He has 60+ publications in peer reviewed international journals with high impact factor and has 2 publications in various International Conferences held in India and abroad. Dr. Kalita has been an expert speaker in various International Conferences and has organized an International Conference (ICNAA-2022, ICNACT 2024, ICNACT 2025). Dr. Kalita was an Invited researcher at Usak Univ., Turkey, 2023. Dr. Kalita has published several issues in Journal of nonlinear and convex analysis, Mathematical notes, Palestine J. Mathematics, Boletim da Sociedade Paranaense de Matemática as a guest editor. He is working on Function spaces, integration theory, measure theory, summability, fixed point theory, and fractal calculus. He published several edited books as an editor. Dr. Kalita has research collaborators in several countries of Europe, USA, Asian and Africa.
Prof. Bipan Hazarika is a Professor at Gauhati Univ., India. Before joining Gauhati Univ. he worked as a Professor at Rajiv Gandhi Univ., India from 2005 to 2018. He received his PhD degree from Gauhati Univ., India. His main research interests include the field of sequences spaces, summability theory, applications of fixed point theory, fuzzy analysis, function spaces of non-absolute integrable functions. He has published over 200 research papers in several international journals. He is regular reviewer of more than 50 different journals published from Springer, Elsevier, Taylor and Francis, Wiley, IOS Press, World Scientific, American Mathematical Society, De Gruyter etc. He has published books on Differential Equations, Differential Calculus and Integral Calculus. He is an editorial board member of more than 5 International Journals and Guest Editor of the special issue “Sequence spaces, Function spaces and Approximation Theory”, Journal of Function Spaces. He has edited five books on different topics of mathematics, out of them two are published by CRC Press and three are published by Springer.
Dr. Ranis Ibragimov is an Associate Professor at Hampton Univ., USA. He earned his Ph.D. from the Univ. of Waterloo (Canada) and has extensive experience as an industry researcher and as an academic faculty member. He previously served as a Professor of Mathematics at Wenatchee Valley Coll., a Hispanic-serving institution. Additionally, he has served as an Associate Professor at the Univ. of Texas at Rio Grande Valley and as a Monbusho Research Fellow at Kyoto Univ. Research Institute of Mathematics in Japan. Furthermore, he was an NSF-supported summer professor at the Pacific Northwest National Laboratory (Department of Energy, WA) in the US. He also worked as a Lead Mathematician at GE Global Research in New York, USA. Dr. Ibragimov’s main area of research is numerical Methods and their applications to mathematical modeling in physical, engineering, and environmental sciences. He is also interested in Lie Group Analysis of Differential Equations.