Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator

Aziz Ur Rehman; Muhammad Riaz; Ilyas Khan; Abdullah Mohamed

doi:10.3934/math.2023414

Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator

Abstract

A new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on the newly introduced Constant Proportional Caputo fractional derivative operator. This fractional model has been solved analytically, and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. For the physical significance of various system parameters such as α , β , Pr , Gr , Gm , Sc on velocity, temperature and concentration profiles, different graphs are demonstrated by Mathcad software. The Constant Proportional Caputo fractional parameter exhibited a retardation effect on momentum and energy profile, but it is visualized that for small values of Casson fluid parameter, the velocity profile is higher. Furthermore, to validated the acquired solutions, some limiting models such as the ordinary Newtonian model are recovered from the fractionalized model. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, from the literature, it is observed that to deriving analytical results from fractional fluid models developed by the various fractional operators is difficult, and this article contributes to answering the open problem of obtaining analytical solutions for the fractionalized fluid models.

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Authors (4)

Aziz Ur Rehman
Muhammad Riaz dr
- Faculty of Applied Physics and Mathematics
- Gdańsk University of Technology
Ilyas Khan
Abdullah Mohamed

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DOI:: Digital Object Identifier (open in new tab) 10.3934/math.2023414
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Keywords

CPC DERIVATIVE, ANALYTICAL SOLUTION, SPECIAL FUNCTIONS, SYSTEM PARAMETERS

Details

Category:

Articles

Type:

artykuły w czasopismach

Published in:

AIMS Mathematics no. 8, pages 8185 - 8209,
ISSN: 2473-6988

Language:

English

Publication year:

2023

Bibliographic description:

Rehman A. U., Riaz M., Khan I., Mohamed A.: Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator// AIMS Mathematics -Vol. 8,iss. 4 (2023), s.8185-8209

DOI: