An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique

Khan, Hassan; Khan, Adnan; Qurashi, Maysaa Al; Băleanu, Dumitru; Shah, Rasool

doi:10.1155/2020/5047054

Cited by 9 publications

(4 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to the effectiveness of fractional order integrals and derivatives, several models in sciences and engineering have been formulated and analyzed successfully (Okyere et al 2016). Fractional order differential operator is non local (Khan et al 2020). This makes fractional differential equation to be veritable tools for modelling marital relations.…”

Section: Nonlinear Dynamical Models In the Study Of Complex Phenomenamentioning

confidence: 99%

Untitled

2020

AJS

View full text Add to dashboard Cite

Mission ATINER is an Athens-based World Association of Academics andResearchers based in Athens. ATINER is an independent and non-profit Association with a Mission to become a forum where Academics and Researchers from all over the world can meet in Athens, exchange ideas on their research and discuss future developments in their disciplines, as well as engage with professionals from other fields. Athens was chosen because of its long history of academic gatherings, which go back thousands of years to Plato's Academy and Aristotle's Lyceum. Both these historic places are within walking distance from ATINER"s downtown offices. Since antiquity, Athens was an open city. In the words of Pericles,Athens"…is open to the world, we never expel a foreigner from learning or seeing". ("Pericles" Funeral Oration", in Thucydides, The History of the Peloponnesian War). It is ATINER"s mission to revive the glory of Ancient Athens by inviting the World Academic Community to the city, to learn from each other in an environment of freedom and respect for other people"s opinions and beliefs. After all, the free expression of one"s opinion formed the basis for the development of democracy, and Athens was its cradle. As it turned out, the Golden Age of Athens was in fact, the Golden Age of the Western Civilization. Education and (Re)searching for the "truth" are the pillars of any free (democratic) society. This is the reason why

show abstract

Section: Nonlinear Dynamical Models In the Study Of Complex Phenomenamentioning

confidence: 99%

Untitled

2020

AJS

View full text Add to dashboard Cite

show abstract

“…Different studies are available in the literature addressing the solution of varying fractional order biological disease models in environments displaying uncertainty. The application of Caputo operator to convey non-integer derivative of fractional order can be found in (Khan et al 2020), handling of chaos control and synchronization of a biological snap oscillator through a new fractional model is addressed with regard to bio-engineering in (Sommacal et al 2008), biology (Toledo-Hernandez et al 2014, (Tokhmpash 2021), signal processing (Gutierrez et al 2010), image processing (Debnath 2003), electronics (Krishna and Reddy 2008) robotics (Singh et al 2021), control theory (Panda and Dash 2006), (Garrappa 2015). Numerical parameters, variables and radiation elements are used for the treatment model's simulation.…”

Section: Introductionmentioning

confidence: 99%

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

View full text Add to dashboard Cite

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.

show abstract

“…Bildik and Deniz [54] employed the Sumudu decomposition method for solving predator-prey systems. Several methods have been used for solving linear and nonlinear biological population models, such as Adomian decomposition method (ADM), Laplace Adomin decomposition method (LADM), reduced differential transform method (RDTM), variation iteration method ( ) VIM [47,[55][56][57]. The detriment of many of the above mentioned strategies is that they are always hierarchical and require a lot of computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Fractional spatial diffusion of a biological population model via a new integral transform in the settings of power and Mittag-Leffler nonsingular kernel

Rashid¹,

Kubra²,

Ullah³

2021

Phys. Scr.

View full text Add to dashboard Cite

The current paper examines some novel and interesting aspects of the fractional biological population model involving the efficacious Atangana-Baleanu fractional derivative operator. It assists us in comprehending the dynamical techniques of population changes in biological population models and generates precise prognostication. This technique correlates with the Elzaki transform method and the homotopy perturbation method. The Elzaki transform is a modification of the classical Fourier Laplace transform. The approximate-analytical solutions of the biological population model are examined using the Elzaki transform homotopy perturbation method (ETHPM). The exact solution of the aforesaid scheme is being investigated in terms of the Mittag-Leffler function. The role of fractional-order on spatial diffusion of a biological population model is demonstrated in two and three-dimensional surface plots. The comparative analysis between exact and numerical solutions reveals the innovative features of the composite fractional derivative in the discussed model. Furthermore, the proposed approach is very powerful, reliable, wellorganized, and pragmatic for fractional PDEs and it might be extended to other physical processes.

show abstract

An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique

Cited by 9 publications

References 38 publications

Untitled

Untitled

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

Fractional spatial diffusion of a biological population model via a new integral transform in the settings of power and Mittag-Leffler nonsingular kernel

Contact Info

Product

Resources

About