UGC Approved Journal no 63975(19)
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ISSN: 2349-5162 | ESTD Year : 2014
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Volume 11 Issue 6
June-2024
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIR2406929


Registration ID:
543793

Page Number

j239-j254

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Title

Fractional Calculus in Mathematical Modelling

Abstract

Abstract: Using fractional calculus modelling the memory effect in the model is allowed. With the present data mathematical models can help to forecast future outbreak of diseases. Depending on the disease of interest, different methods and more convenient methods are to be a Studying the dynamics of predator-prey model consisting of spatial interactions among the prey, intermediate predator and the top predator as well as formulating and analysing a new mathematical model for COVID-19 epidemic is the main target. A new model for COVID-19 epidemic with isolated class in fractional order is formulated and analysed. Main objective of ‘ Disease Modelling using Fractional Differential Equations and Estimation’ is to show that FDEs based on concrete examples and experimental data may model more effectively specific problems than ODEs. By using the Caputo- Fabrizio fractional operator the SIRS-SI malaria model is modified for memory effect inclusion . Focusing on reviewing the results of epidemiological modelling including fractional susceptible-Infective-Recovered SIR, SEIR, SEIR model is one objective of this paper. The fixed point theory is used on a paper to examine the existence and uniqueness of solution of the considered fractional SIRS-SI model describing the spreading of malaria. Various methods for approximate solutions of system of non linear differential equations such as Finite decomposition method (FDM), Variational interation method (VIM), Finite element method (FEM), Adomian decomposition method (ADM), Homotopy perturbation method (HPM), Homotopy analysis method (HAM) are applied on another paper. To explore the transmission of chlamydia, various modelling has been presented and mathematical modelling of chlamydia trachomatis in human carrier was introduced. Fractional calculus is used to depict on SEIR model with a system of fractional –order differential equations. The modified hybrid Nelder Mead Simplex search and particle swarm optimization ( MH-NMSS-PSO) algorithm to estimate the parameters for fractional DEs and the multi- term – fractional DEs are employed. An optimal control system for the mosaic epidemic in terms of Caputo fractional derivatives is derived. The generalized Euler method (GEM) is found to be powerful, effective and reliable method for investigation of fractional mathematical model. The multi- term fractional SEIAR model provides better fit to the real data than the integer order and single term fractional SEIAR models. A new mathematical model for COVID-19 epidemic with isolated class helps to understand the mechanism of the transmission , characteristics of diseases and to protect population health. A fractional SIRS-SI malaria model transmission along with a no. of cures is studied. It is predicted that the proposed fractional calculus model provides a wide scope for analysing diseases scientifically. The results of epidemiology modelling mainly for the fractional epidemic model is reviewed such as mathematical modelling of dengue epidemic (SIR-SI MODEL), mathematical modelling of HIV/AIDS epidemic (SIJA MODEL).

Key Words

Key words: Predator, Chlamydia, mathematical model, COVID-19, SIR, special function , asymptotically stable, compartmental model.

Cite This Article

"Fractional Calculus in Mathematical Modelling", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 6, page no.j239-j254, June-2024, Available :http://www.jetir.org/papers/JETIR2406929.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"Fractional Calculus in Mathematical Modelling", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 6, page no. ppj239-j254, June-2024, Available at : http://www.jetir.org/papers/JETIR2406929.pdf

Publication Details

Published Paper ID: JETIR2406929
Registration ID: 543793
Published In: Volume 11 | Issue 6 | Year June-2024
DOI (Digital Object Identifier):
Page No: j239-j254
Country: Imphal west, Manipur, India .
Area: Applied Mathematics
ISSN Number: 2349-5162
Publisher: IJ Publication


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