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Mittag-Leffler functions with heavy-tailed distributions' algorithm based on different biology datasets to be fit for optimum mathematical models' strategies

dc.authorscopusid 7005872966
dc.authorscopusid 56585856100
dc.contributor.author Baleanu, D.
dc.contributor.author Karaca, Y.
dc.contributor.authorID 56389 tr_TR
dc.contributor.other Matematik
dc.date.accessioned 2024-02-23T10:38:24Z
dc.date.available 2024-02-23T10:38:24Z
dc.date.issued 2022
dc.department Çankaya University en_US
dc.department-temp Baleanu D., Çankaya University, Ankara, Turkey, Institute of Space Science, Bucharest, Magurele, Romania; Karaca Y., University of Massachusetts Medical School, Worcester, MA, United States en_US
dc.description.abstract Complexity of living organisms owing to their inherent functional properties points toward a systems biology approach due to the fact that structural and topological uncertainties exist along with abrupt transitions characterized by unknown inputs, time-varying parameters and unpredictable observation states. The related uncertain, emergent and evolving qualities of organisms along with their varying quantities and states present in the related complex system need to be identified in biological datasets based on mathematical models in a way that enables the structural identification analysis in a reasonable time frame, the detection of nonlinear dependencies among the many parameters involved and practical analysis for the identification of data at stake. Superstatistics, which is concerned with the study of nonlinear systems, has proven to be a significant tool to examine the dynamic aspects of organisms, substances, particles and other biological elements. Superstatistics is characterized by the superposition of varying statistical models to achieve the desired nonlinearity. The challenge of integrating fractional calculus in cases of complexity requires an effective use of empirical, numerical, experimental and analytical methods to tackle complexity. One of the most noteworthy tools in the fractional calculus context is the Mittag-Leffler (ML) functions. Mittag-Leffler distributions have extensive application domains when dealing with irregular and nonhomogeneous environments for dynamic problems' solutions. These distributions can be used in reliability modeling as an alternative for exponential distribution; and thus, the proposed integrated approach in this study addresses the Mittag-Leffler (ML) function with two parameters (α,β) in order to investigate the dynamics of diseases related to biological elements. Arising in the different solutions of varying complex biological systems, ML function generalizes the exponential function; and to this end, firstly, we applied the ML function with two parameters to biological datasets (cancer cell dataset and diabetes dataset, namely raw datasets) in order to obtain the new datasets (ml_cancer cell dataset and ml_diabetes dataset) with significant attributes for diagnosis, prognosis and classification of diseases. Secondly, heavy-tailed distributions (The Mittag-Leffler distribution, Pareto distribution, Cauchy distribution and Weibull distribution) were applied to the new datasets obtained, and their comparison was made with regard to the performances, by employing the log likelihood value (MLE) and the Akaike Information Criterion (AIC). Fitting algorithm Mittag-Leffler function is based on heavy-tailed distributions. Subsequently, the ML functions that represent the cancer cell and diabetes data were identified so that the two parameters Eα,β(z) yielding the optimum value based on the distributions fit could be found. By finding the most significant attributes with heavy-tailed distributions (The Mittag-Leffler distribution, Pareto distribution, Cauchy distribution and Weibull distribution) based on Mittag-Leffler function with two parameters (α,β) the diagnosis, prognosis and classification of the diseases has been enabled in our study. In this way, through this proposed integrative scheme, optimal strategical means have been obtained for accurate and robust mathematical models' strategies concerning the diagnosis and progress of the diseases. The results obtained by the current study for diseases on biological datasets based on mathematical models demonstrate that the integrative approach with Mittag-Leffler with heavy-tailed distributions algorithm is applicable and fits very well to the related data with the robust parameters' values observed and estimated in transient chaotic and unpredictable settings. The analysis results obtained by the data fitting algorithm scheme proposed have demonstrated its criticality for understanding the dynamics of transmission and prevalence operating in the complex biological and epidemiological systems along the Mittag-Leffler function based on distribution scale, with temporal and spatial attributes, to improve applicability and accuracy constituting optimal mathematical models' strategies. © 2022 Elsevier Inc. All rights reserved. en_US
dc.identifier.citation Baleanu, Dumitru; Karaca, Yeliz. "Mittag-Leffler functions with heavy-tailed distributions' algorithm based on different biology datasets to be fit for optimum mathematical models' strategies", in Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems, Academic Press, pp. 117-132, 2022. en_US
dc.identifier.doi 10.1016/B978-0-323-90032-4.00011-0
dc.identifier.endpage 132 en_US
dc.identifier.isbn 9780323900324
dc.identifier.isbn 9780323886161
dc.identifier.scopus 2-s2.0-85137866154
dc.identifier.scopusquality N/A
dc.identifier.startpage 117 en_US
dc.identifier.uri https://doi.org/10.1016/B978-0-323-90032-4.00011-0
dc.identifier.wosquality N/A
dc.institutionauthor Baleanu, Dumitru
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.relation.ispartof Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems en_US
dc.relation.publicationcategory Kitap Bölümü - Uluslararası en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 4
dc.subject Complexity en_US
dc.subject Data Analysis en_US
dc.subject Data Fitting en_US
dc.subject Dynamic Biological Models en_US
dc.subject Fractional Calculus en_US
dc.subject Heavy-Tailed Distributions en_US
dc.subject Mathematical Biology en_US
dc.subject Mittag-Leffler Function en_US
dc.subject Nonhomogeneous Systems And Nonlinearity en_US
dc.subject Superstatistics en_US
dc.title Mittag-Leffler functions with heavy-tailed distributions' algorithm based on different biology datasets to be fit for optimum mathematical models' strategies tr_TR
dc.title Mittag-Leffler Functions With Heavy-Tailed Distributions' Algorithm Based on Different Biology Datasets To Be Fit for Optimum Mathematical Models' Strategies en_US
dc.type Book Part en_US
dspace.entity.type Publication
relation.isAuthorOfPublication f4fffe56-21da-4879-94f9-c55e12e4ff62
relation.isAuthorOfPublication.latestForDiscovery f4fffe56-21da-4879-94f9-c55e12e4ff62
relation.isOrgUnitOfPublication 26a93bcf-09b3-4631-937a-fe838199f6a5
relation.isOrgUnitOfPublication.latestForDiscovery 26a93bcf-09b3-4631-937a-fe838199f6a5

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