This book focuses on the fundamental processes involved in calcium signaling through fractional mathematical modeling. The intended reader of the book is mathematically proficient students of cell biology, applied mathematics and mathematical biology who are interested in learning about modeling in cell biology. The book inspires the graduate students and researchers to collaborate with experimentalists while studying the direction needed to explore the modeling literature. Organized into four chapters, the book introduces fractional calculus and is devoted to understanding the receptor activation by the ligand, that is Thrombin via fractional model incorporating the Caputo-Fabrizio fractional operator. It studies the calcium profile in red blood cells with the help of the advection-diffusion equation. The book further studies the process of buffering, aiding the lowering of the calcium concentration in the cytosol, which rises due to calcium influx from extracellular space and intracellular storage. It explains the concept of anomalous diffusion-a mathematical model is proposed to characterize the anomalous subdiffusion of cytosolic calcium.

Autorentext

Ritu Agarwal is Assistant Professor at the Malaviya National Institute of Technology, Jaipur, Rajasthan. She holds M.Sc., M.Phil. and Ph.D. degrees in Mathematics from the University of Rajasthan, Jaipur, India. She was awarded Junior Research Fellowship and Senior Research Fellowship from CSIR, India. Her research interests are in bicomplex analysis, fractional calculus, geometric function theory and mathematical modeling. She is Life Member of several professional bodies including the Indian Mathematical Society, Ramanujan Mathematical Society and Indian Science Congress Association, affiliate member of the American Mathematical Society (AMS). She is a reviewer for MathSciNet and many SCI/SCOPUS indexed journals. She has guided more than 24 M.Sc. dissertations and 8 Ph.D. students. She has published more than 80 research papers in journals of repute. She has completed one NBHM (DAE) and two TEQIP-III-funded research projects in her area of specialization. She has authored various textbooks on engineering mathematics, including Discrete Mathematical Structures, and edited a book, Mathematical Modeling and Soft Computing in Epidemiology.

Sunil Dutt Purohit is Associate Professor of Mathematics at Rajasthan Technical University (RTU), Kota, India. He is also Associate Dean of Academic Affairs and Associate Dean of Applied Sciences at the same university. He did his M.Sc. and Ph.D. in Mathematics from Jai Narayan Vyas University, Jodhpur, India. He was awarded the Gold Medal for being the topper in the M.Sc. examination and then awarded Junior Research Fellowship and Senior Research Fellowship from the Council of Scientific and Industrial Research (CSIR), India. His research interests include topics on special functions, basic hypergeometric series, fractional calculus, geometric function theory, mathematical analysis and mathematical modeling. He has published more than 200 research articles in reputable national and international journals, with SCI and Scopus indexing, as well as authored 10 books. From April 2018 until March 2023, he also held the position of General Secretary for the Rajasthan Ganita Parishad.

Kritika is Lecturer at Government Polytechnic College, Sikar, Rajasthan, under the Technical Education Department of Rajasthan, India. She holds an M.Sc. degree in Mathematics from the University of Rajasthan, Jaipur, India, and a Ph.D. in Mathematics from the Malaviya National Institute of Technology, Jaipur, India. She has research interests in fractional calculus and mathematical modeling.