A comparative analysis of plasma dilution based on fractional integro-differential equation: an application to biological science

ABSTRACT

Plasma dilution is an important factor of a human proteome specifically from hemostatic balance to coagulation process. This manuscript presents a mathematical analysis of integro-differential equation model of plasma dilution model. The integro-differential equation of plasma dilution is modeled via three types of fractional operators namely Atangana-Baleanu, Caputo and Caputo-Fabrizio based on the comparison of non-singular and non-local kernels. The fractionalized integro-differential equation of plasma dilution is solved by invoking Laplace transform method corresponding with physical conditions on plasma dilution model. The lengthy and cumbersome calculations of governing equation namely integro-differential equation of plasma dilution is expressed in the format of generalized hyper-geometric function ${\hspace{0.17em}}_1^{\hspace{0.17em}}{\mathbf{\Psi }}_2^{\hspace{0.17em}}\left(z\right)$ and elementary functions. The graphical illustration for plasma dilution model has been depicted for embedded parameters as involved in the governing equation. The comparative analysis of three types of fractional approaches showed a good adaptability in describing pharmacokinetic responses which reflect the crystalloid infusion period as well.

KEYWORDS:

• Plasma dilution model
• modern fractional approaches
• analytic solutions
• generalized hyper-geometric function

Acknowledgments

The author Kashif Ali Abro is highly thankful and grateful to Mehran university of Engineering and Technology, Jamshoro, Pakistan for generous support and facilities of this research work. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Kashif Ali Abro

Dr. Kashif Alli Abro received his Bachelor’s degree in Mathematics from University of Sindh Jamshoro Pakistan, and M.Phil. and PhD in Applied Mathematics from the NED University of Engineering and Technology, Karachi, Pakistan. Whilst he did his post doctorate in Applied Mathematics from the University of the Free State, Bloemfontein, South Africa. He is presently working as an Assistant Professor in the Department of Basic Sciences and related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan. His research interests are: Fractional Calculus (Modern Fractional Operators) and Modern Control Engineering. He is also author of 100 plus international research papers having 300 plus impact factor as per journal citation report 2020.

Abdon Atangana

Dr. Abdon Atangana received his B.Sc. Bachelor (Pure Mathematics), B.Sc. Honors (Applied Mathematics), M.Sc. (Applied Mathematics), PhD (Geohydrology) from University of the Free State South Africa. He is currently a full research professor at the Faculty of Natural and Agriculture Science in University of the Free State South Africa. His research interests are fractional calculus and control system identifications.

J.F. Gómez-Aguilar

Dr. J. F. Gómez-Aguilar received the B.S. degree and M. Eng., in electrical engineering from Guanajuato University in 2005 and 2007, respectively, and Ph.D. degree in Physical from DCI, Guanajuato University in 2012. He is member of the Science and Technology National Council Engineering and Industry Recognized Referees Record (CONACYT-RCEA MEXICO). He is currently a full research professor at the Electronics Engineering Department of the National Research and Technological Development Center (CENIDET), Cuernavaca, Mor., Mexico. His scientific interests are fractional calculus, image and signal processing, control, electrochemistry, bioelectromagnetism and biomedical applications. He is serving as guest editor of some special issues, and also reviewer of more than 40 international accredited journals. He has presented and participated in more than 10 international conferences, also is author of more than 100 papers published in international journals with strict revision. His research interests are nonlinear dynamics, control theory, computational complexity, fractional dynamics, iterative methods, integral transforms and applications, signal processing, biomathematics, mathematical physics and variable order fractional calculus and applications.