https://doi.org/10.1140/epjp/s13360-021-01610-w
Regular Article
On a reaction–diffusion model for calcium dynamics in neurons with Mittag–Leffler memory
Department of Mathematics, School of Technology, Pandit Deendayal Energy (Petroleum) University, 382007, Raisan, Gandhinagar, India
Received:
7
April
2021
Accepted:
26
May
2021
Published online:
4
June
2021
In recent times, the Atangana–Baleanu–Caputo (ABC) derivative is one of the robust fractional operators to solve complex dynamical problems due to its nonlocal and non-singular Mittag–Leffler kernels. In this paper, calcium dynamics in neurons are described by a time-fractional reaction–diffusion model with calcium-binding proteins and analyzed analytically. Here, we use the ABC derivative to assess the impact of calcium-binding proteins on calcium dynamics along with the index of its derivative. The Laplace transform and exponential Fourier transform of ABC derivative are used to obtaining the approximate analytical solutions in terms of generalized Mittag–Leffler function. The results are illustrated graphically to study some interesting phenomena of calcium dynamics with the influence of the ABC operator. From the graphical results, it is observed that the high concentration occurs near the source and excess calcium-binding proteins significantly decrease the concentration of the cells. Also, the results show that the ABC operator provides better control to portray the concentration profile due to the Mittag–Leffler memory.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
