On the integral transform of Mittag-Leffler-type functions with applications

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anupama Choudhary ◽  
Devendra Kumar ◽  
Jagdev Singh
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Integral Transform ◽  
Natural Manner ◽  
Models In Science

Abstract In this article, we study certain results connected with a generalized Mittag-Leffler function. A generalized Mittag-Leffler function operator of Laplace and Sumudu conversions are investigated and some applications of the recognized results are also deduced as corollaries in this article. The outcomes of the present study are valuable in solving fractional order mathematical models in science, mathematics, finance and technology where the Mittag-Leffler function arises in a natural manner.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

Fractional-Order Modeling and Simulation of Magnetic Coupled Boost Converter in Continuous Conduction Mode

2018 ◽  
Vol 28 (05) ◽  
pp. 1850061 ◽  
Author(s):  
Zirui Jia ◽  
Chongxin Liu
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Fractional Order ◽  
Transfer Functions ◽  
Circuit Simulation ◽  
Boost Converter ◽  
Averaged Model ◽  
Conduction Mode ◽  
State Average ◽  
Continuous Conduction Mode

By using fractional-order calculus theory and considering the condition that capacitor and inductor are naturally fractional, we construct the fractional mathematical model of the magnetic coupled boost converter with tapped-inductor in the operation of continuous conduction mode (CCM). The fractional state average model of the magnetic coupled boost converter in CCM operation is built by exploiting state average modeling method. In these models, the effects of coupling factor, which is viewed as one generally, are directly pointed out. The DC component, the AC component, the transfer functions and the requirements of the magnetic coupled boost converter in CCM operation are obtained and investigated on the basis of the state averaged model as well as its fractional mathematical model. Using the modified Oustaloup’s method for filter approximation algorithm, the derived models are simulated and compared using Matlab/Simulink. In order to further verify the fractional model, circuit simulation is implemented. Furthermore, the differences between the fractional-order mathematical models and the corresponding integer-order mathematical models are researched. Results of the model and circuit simulations validate the effectiveness of theoretical analysis.

scholarly journals Mathematical Models of Microbial Growth and Metabolism: A Whole-Organism Perspective

2017 ◽  
Vol 100 (4) ◽  
pp. 343-362
Author(s):  
Olga A. Nev ◽  
Hugo A. Van Den Berg
Keyword(s):  
Mathematical Models ◽  
Microbial Growth ◽  
Regulation Of Gene Expression ◽  
Dynamic Allocation ◽  
Natural Manner ◽  
Additional Information ◽  
Nutrient Assimilation ◽  
Mode Of Life ◽  
Metabolic Activities ◽  
Micro Organisms

We review the principles underpinning the development of mathematical models of the metabolic activities of micro-organisms. Such models are important to understand and chart the substantial contributions made by micro-organisms to geochemical cycles, and also to optimise the performance of bioreactors that exploit the biochemical capabilities of these organisms. We advocate an approach based on the principle of dynamic allocation. We survey the biological background that motivates this approach, including nutrient assimilation, the regulation of gene expression, and the principles of microbial growth. In addition, we discuss the classic models of microbial growth as well as contemporary approaches. The dynamic allocation theory generalises these classic models in a natural manner and is readily amenable to the additional information provided by transcriptomics and proteomics approaches. Finally, we touch upon these organising principles in the context of the transition from the free-living unicellular mode of life to multicellularity.

scholarly journals Some new mathematical models of the fractional-order system of human immune against IAV infection

2020 ◽  
Vol 17 (5) ◽  
pp. 4942-4969 ◽  
Author(s):  
H. M. Srivastava ◽  
◽  
Khaled M. Saad ◽  
J. F. Gómez-Aguilar ◽  
Abdulrhman A. Almadiy ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Fractional Order System ◽  
Order System ◽  
Human Immune

scholarly journals On the Volterra-Type Fractional Integro-Differential Equations Pertaining to Special Functions

2020 ◽  
Vol 4 (3) ◽  
pp. 33
Author(s):  
Yudhveer Singh ◽  
Vinod Gill ◽  
Jagdev Singh ◽  
Devendra Kumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Hypergeometric Function ◽  
Fractional Order ◽  
Integral Transform ◽  
Special Functions ◽  
Confluent Hypergeometric Function ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Volterra Type

In this article, we apply an integral transform-based technique to solve the fractional order Volterra-type integro-differential equation (FVIDE) involving the generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function in terms of several complex variables in the kernel. We also investigate and introduce the Elazki transform of Hilfer-derivative, generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function. In this article, we have established three results that are present in the form of lemmas, which give us new results on the above mentioned three functions, and by using these results we have derived our main results that are given in the form of theorems. Our main results are very general in nature, which gives us some new and known results as a particular case of results established here.

Time-Fractional Hygrothermoelastic Problem for a Sphere Subjected to Heat and Moisture Flux

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Xue-Yang Zhang ◽  
Yi Peng ◽  
Xian-Fang Li
Keyword(s):  
Heat Conduction ◽  
Fractional Order ◽  
Integral Transform ◽  
Moisture Diffusion ◽  
Moisture Flux ◽  
Moisture Distribution ◽  
Order Derivative ◽  
Transform Method ◽  
Stress Components ◽  
Heat And Moisture

In this paper, a non-Fourier model of heat conduction and moisture diffusion coupling is proposed. We study a hygrothermal elastic problem within the framework of time-fractional calculus theory for a centrally symmetric sphere subjected to physical heat and moisture flux at its surface. Analytic expressions for transient response of temperature change, moisture distribution, displacement, and stress components in the sphere are obtained for heat/moisture flux pulse and constant heat/moisture flux at the sphere's surface, respectively, by using the integral transform method. Numerical results are calculated and the effects of fractional order on temperature field, moisture distribution, and hygrothermal stress components are illustrated graphically. Subdiffusive and super-diffusive transport coupling behavior as well as wave-like behavior are shown. When fractional-order derivative reduces to first-order derivative, the usual heat and moisture coupling is recovered, which obeys Fourier heat conduction and Fick's moisture diffusion.

Some Mathematical Models in Science

Science ◽  
1969 ◽  
Vol 166 (3906) ◽  
pp. 695-699 ◽  
Author(s):  
M. Kac
Keyword(s):  
Mathematical Models ◽  
Models In Science
Sign in / Sign up

Export Citation Format

Share Document