Abstract Optimal control theory is an extension of the calculus variations. It a mathematical optimization method for deriving strategies dynamic system. In this paper, system differential equations which we aim to utilize TikTok, one most attractive internet platforms. TikTok has garnered immense popularity, surpassing other social media However, its addictive nature raised concerns about mental health, including depression, eating disorders, anxiety, self-obsession, and narcissistic...

In order to improve results, this work investigates how the Freelance Model (FM), Fractional Derivative (FD), and Artificial Neural Network (ANN) may all function together. We suggest a new method that combines varied skills of freelancers with precision fractional derivatives adaptability neural networks maximize benefits each. This proposed strategy provides perspective computational methodologies holds promising impact on diverse industries. Future developments applications can be made...

As technology advances and the Internet makes our world a global village, it is important to understand prospective career of freelancing. A novel symmetric fractional mathematical model introduced in this study describe competitive market freelancing significance information its acceptance. In study, fixed point theory applied analyze uniqueness existence freelance model. Its numerical solution derived using Euler’s method, each case has been presented graphically as well tabular. Further,...

Dengue is a complex disease because of the link it forms between humans, mosquitoes, and several virus serotypes, including efficient strategies for vector survival strategies.For this reason, understanding various factors that influence recurrence has been an inescapable fight policy makers scientists alike.In paper, susceptible-infected-recovered (SIR) model dengue fever presented solved by incorporating new technique called Perturbation Iteration Algorithm (PIA).Through method, solution...

In this paper, DSEK model with fractional derivatives of the Atangana‐Baleanu Caputo (ABC) is proposed. This paper gives a brief overview ABC derivative and its attributes. Fixed point theory has been used to establish uniqueness existence solutions for model. According theory, we will define two operators based on Lipschitzian prove that they are contraction mapping relatively compact. Ulam‐Hyers stability theorem implemented model’s in Banach space. Also, Euler’s numerical method derived...

Water pollution is a major global problem that requires ongoing evaluation and revision of water resource policies at all levels, in order to create healthy living environment.Differential equations are an effective way analyze such situations.In this paper system linear with interconnecting pipes considered for analyzing the lakes through differential equations.Perturbation-iteration method used compute approximate solution three input models i.e. periodic, step model exponentially decaying...

In this paper, a new integral‐type transformation is being introduced, which the generalization of Laplace and Fourier transform. This integral transform named as “Fareeha transform.” It successfully applied on ordinary differential equation to show its efficacy simplicity. Also, possible applications Fareeha in control theory, electric circuits, data compression have been discussed detail.

Financial derivatives plays a major role in all financial deals these days. Black–Scholes option pricing model gives risk free analysis for investing options. In the current work, method called Laplace Perturbation Iteration Algorithm is being applied on Fractional Equation to obtain its fractional analytical solutions series form analyze results European and American problem, quickly accurately. incorporates transform forms an iterative scheme that derives without any inconvenience. The...

Minerals and nutrients are vital to life, but their excess can harm health sometimes lead life risks. Harmful impact of in water be a threat marine as well. Waquoit Bay linked with its eight rivers ponds is becoming the reason for nutrient passage into Bay. Excess amounts were found from coastal areas therefore analyzed this work by system nine differential equations. The main objective paper develop mathematical model assess situation pollution suggest some solutions using optimal control...

Game theory is an excellent mathematical tool to describe the interaction between immune system and cancerous leukocytes (c.leu). The feature of differentiate mutate give rise leukemia in domain ecological models as well. In this work, dynamic described compared by two models: firstly a simple probabilistic model using zero-sum player game Hawk Dove, secondly Leslie Predator Prey ecology. main goal study compare results both then discuss treatment i.e., Hematopoietic Stem cell transplant...

This work is based on the implementation of an iterative perturbation method to attain series solutions nonlinear fractional differential difference equation (NFDΔE). Perturbation‐iteration algorithm (PIA) assigns a parameter ϵ all terms and converts it into simple (FDΔE). By simply solving this FDΔE, can be obtained. To show efficacy accuracy method, three famous NFDΔE, i.e, Lotka‐Volterra equation, discrete KdV discretized mKdV lattice will solved numerically via PIA. Also, comparison...

During the past few years, freelancing has grown exponentially due to pandemic and subsequent economical changes in world. In fact, last ten a drastic increase been observed; people quit their jobs be own boss. There are various reasons for this: downsizing of employees, not having fun jobs, unemployment, part time work earn more, etc. Observing this vast change, many individuals on Facebook/YouTube, NGOs, government departments started teaching as course; date, thousands youngsters have...

In this work successive differentiation method is applied to solve highly nonlinear partial differential equations (PDEs) such as Benjamin–Bona–Mahony equation, Burger's Fornberg–Whitham and Gardner equation. To show the efficacy of new technique, figures have been incorporated compare exact solution results method. Wave variable used convert PDE into ordinary equation with order reduction. Then utilized obtain numerical considered PDEs in paper. Copyright © 2017 John Wiley & Sons, Ltd.

During worldwide epidemic of COVID-1, people started to depend on social media apps cure their boredom. It was beneficial provide information easily a wide audience. The increased time spent phones led many, including teenagers and children, becoming addicted media, particularly TikTok. As result, this usage TikTok became an itself. Therefore, in work, fractional mathematical model is being developed analyze the influence human population different ages. In paper, two equilibrium points for...

The fundamental idea of this work is to modify Descemet’s Stripping Endothelial Keratoplasty DSEK mathematical model by incorporating the Zernike polynomial examine Higher Order Aberrations (HOA). This has been developed in a way that can identify type aberration occurring after keratoplasty. Model variables are compared with data available already published literature. Surgically induced (HOA) and change corneal power main outcome measures. Eye illness their treatments have always an...

The aim of this research was to relate two physical effects for partial differential equations on the time-coordinate, notably multipledelay times and fractional-derivative. Time Fractional Delay Partial Differential Equations (TFDPDEs) usually interpret some complex phenomenon. This study works solve TFDPDE with shrinking in x proportional delays t numerically by utilizing fractional derivative Caputo sense numerical method known as Perturbation Iteration Algorithm (PIA). A few famous...