Algorithmic Complexity-Based Fractional-Order Derivatives in Computational Biology

Karaca, Yeliz; Băleanu, Dumitru

doi:10.1007/978-981-19-0179-9_3

Cited by 4 publications

(5 citation statements)

References 54 publications

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“…x > 0, 0 < α ≤ 1 (4) The ML distribution has different shapes and distributional properties (see (Mainardi and Gorenflo 2000), (Mittag-Leffler 1903), (Pillai and Functions 1990), (Karaca and Baleanu 2022a) for further related details.…”

Section: Cauchy Distribution: a Continuous Probability Distributionmentioning

confidence: 99%

“…Figure 3 shows the functions along with the four related heavy tailed distributions. The computations were conducted by Matlab with the pattern of [ ] = gml_ f un( ), made for the evaluation pertaining to the MLF (Petrás 2011), (Karaca and Baleanu 2022a).…”

Section: Cauchy Distribution: a Continuous Probability Distributionmentioning

confidence: 99%

“…Factorials, for example, make up only natural numbers, so this has constricting factors for its domains of applications (Herrmann 2011). Gamma function is introduced for any as factorial generalization, indicated as in (Karaca and Baleanu 2022a) can be generalized as well through the replacement of its factorial component with a gamma function, producing the following in accordance with Eq. ( 5).…”

Section: The Basic Theory Behind the Fractional Calculusmentioning

confidence: 99%

“…Algorithm 1 has been benefited from for the fitting with three parameters related to MLF based on heavy-tailed distributions. The related steps for Algorithm 1 can be referred to in (Karaca and Baleanu 2022a).…”

Section: Computation-related Application Of ML Functions With Heavyta...mentioning

confidence: 99%

See 3 more Smart Citations

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Karaca

2023

Chaos Theory and Applications

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Neural networks and fractional order calculus are powerful tools for system identification through which there exists the capability of approximating nonlinear functions owing to the use of nonlinear activation functions and of processing diverse inputs and outputs as well as the automatic adaptation of synaptic elements through a specified learning algorithm. Fractional-order calculus, concerning the differentiation and integration of non-integer orders, is reliant on fractional-order thinking which allows better understanding of complex and dynamic systems, enhancing the processing and control of complex, chaotic and heterogeneous elements. One of the most characteristic features of biological systems is their different levels of complexity. In view of this, chaos theory seems to be one of the most applicable areas of life sciences along with nonlinear dynamic and complex systems of living and non-living environment. Biocomplexity, with multiple scales ranging from molecules to cells and organisms, addresses complex structures and behaviors which emerge from nonlinear interactions of active biological agents. This sort of emergent complexity is concerned with the organization of molecules into cellular machinery by that of cells into tissues as well as that of individuals to communities. Healthy systems sustain complexity in their lifetime and are chaotic, so complexity loss or the chaos loss results in diseases. Within the mathematics-informed frameworks, fractional-order calculus based Artificial Neural Networks (ANNs) can be employed for accurate understanding of complex biological processes. This approach aims at achieving optimized solutions through the maximization of the model’s accuracy and minimization of computational burden and exhaustive methods. Within this framework with highly intricate complex elements, computational complexity becomes prominent. Relying on a transdifferentiable mathematics-informed framework and multifarious integrative methods concerning computational complexity, this study aims at establishing an accurate and robust model based upon integration of fractional-order derivative and ANN for the diagnosis and prediction purposes for cancer cell whose propensity exhibits various transient and dynamic biological properties. The other aim is concerned with showing the significance of computational complexity for obtaining the fractional-order derivative with the least complexity in order that optimized solution could be achieved. The multifarious scheme of the study, by applying fractional-order calculus to optimization methods, the advantageous aspect concerning model accuracy maximization has been demonstrated through the proposed method’s applicability and predictability aspect in various domains manifested by dynamic and nonlinear nature displaying different levels of complexity.

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Section: Cauchy Distribution: a Continuous Probability Distributionmentioning

confidence: 99%

Section: Cauchy Distribution: a Continuous Probability Distributionmentioning

confidence: 99%

Section: The Basic Theory Behind the Fractional Calculusmentioning

confidence: 99%

Section: Computation-related Application Of ML Functions With Heavyta...mentioning

confidence: 99%

See 2 more Smart Citations

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Karaca

2023

Chaos Theory and Applications

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“…In recent years, the field of fractional derivatives has emerged as a promising approach to model and understand complex biological processes characterized by non-integer order dynamics [21,27,35]. This unique mathematical framework has found diverse applications in various areas of biology, where traditional integer-order calculus falls short in capturing the intricacies of these systems [6,25].…”

Section: Introductionmentioning

confidence: 99%

Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

Zaitri,

Zitane,

Torres

2023

Computers in Biology and Medicine

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A Computational Analysis Fractional Complex-Order Values by Abc Operator and Mittag-Leffler Kernel Modeling

El-Shorbagy¹,

Rahman²,

Karaca³

2023

Fractals

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A random arbitrary-order mathematical system is investigated via the global and non-singular kernel of Atangana–Baleanu in the sense of Caputo [Formula: see text] derivative in this study where the proposed problem is divided into four general compartments for the explanation. To show the existing result, the Krasnosilkii’s theorem from the theory of fixed points is used, whereas the well-known Banach theorem is utilized in order to show that the solution is unique to the proposed problem. Furthermore, by using the idea of Hyers–Ulam (UH) stability, the generalized problem is perturbed little for the purpose of checking its stability. The numerical solution is evaluated by applying the Adams–Bashforth iterative techniques. The numerical examples derived are tested in order to illustrate the established outcomes along with the numerical simulation to demonstrate the verification of the results obtained. The dynamics of every compartment is examined on different non-integer order ɓ and by choosing arbitrary time [Formula: see text] by the taken approximate solution employing the AB numerical technique. Ultimately, the total continuous spectrum on the dynamics of each quantity in any arbitrary order lying between any of the two natural values, namely 0 and 1, has been achieved based on the investigated analyses.

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Algorithmic Complexity-Based Fractional-Order Derivatives in Computational Biology

Cited by 4 publications

References 54 publications

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

A Computational Analysis Fractional Complex-Order Values by Abc Operator and Mittag-Leffler Kernel Modeling

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