Existence and uniqueness results for mixed derivative involving fractional operators

Elaiw, Abeer Al; Hafeez, Farva; Jeelani, Mdi Begum; Awadalla, Muath; Abuasbeh, Kinda

doi:10.3934/math.2023371

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…To examine the crossover properties, we introduce several notions such as fractal-fractional derivative, fractional order derivative with singular and non-singular kernels, and some other forms of derivative operators. For example, [33,[57][58][59] refers to some valuable work on nonlocal operators and their applications, [34] refers to a mathematical model under the Caputo-Fabrizio operator, [35] refers to fractional dynamics of cellulose degradation, [36] refers to local and nonlocal operators with applications, and [37] refers to existence and uniqueness with applications to epidemiology. Although randomness considerations in the framework of the stochastic equation produce more realistic results, the crossover dynamical behavior has not been studied [38].…”

Section: Of 19mentioning

confidence: 99%

Analyzing a SEIR-Type Mathematical Model of SARS-COVID-19 Using Piecewise Fractional Order Operators

Alharthi¹,

Jeelani²

2023

Preprint

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The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

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Section: Of 19mentioning

confidence: 99%

Analyzing a SEIR-Type Mathematical Model of SARS-COVID-19 Using Piecewise Fractional Order Operators

Alharthi¹,

Jeelani²

2023

Preprint

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“…It is amazing how random events affect everything in the real world, even the movements of people and animals. Some interesting work on different biological models can be studied in [34][35][36][37][38][39][40]. This impact is mathematically interpreted in terms of stochastic models.…”

Section: Introductionmentioning

confidence: 99%

Study of Rotavirus Mathematical Model Using Stochastic and Piecewise Fractional Differential Operators

Alharthi,

Jeelani

2023

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This manuscript is related to undertaking a mathematical model (susceptible, vaccinated, infected, and recovered) of rotavirus. Some qualitative results are established for the mentioned challenging childhood disease epidemic model of rotavirus as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractal calculus. We compute the boundedness positivity of the solution of the proposed model. Additionally, the basic reproduction ratio and its sensitivity analysis are also performed. The global stability of the endemic equilibrium point is also confirmed graphically using some available values of initial conditions and parameters. Sufficient conditions are deduced for the existence theory, the Ulam–Hyers (UH) stability. Specifically, the numerical approximate solution of the rotavirus model is investigated using efficient numerical methods. Graphical presentations are presented corresponding to a different fractional order to understand the transmission dynamics of the mentioned disease. Furthermore, researchers have examined the impact of lowering the risk of infection on populations that are susceptible and have received vaccinations, producing some intriguing results. We also present a numerical illustration taking the stochastic derivative of the proposed model graphically. Researchers may find this research helpful as it offers insightful information about using numerical techniques to model infectious diseases.

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“…For example, in [18][19][20][21][22], the authors investigated the existence of solutions to fractional differential equations by mixing Riemann-Liouville and Caputo fractional derivatives. In [23], the authors studied the existence and uniqueness results for mixed derivatives involving two fractional operators. In [24], the authors studied Hyers-Ulam stability for a class of impulsive coupled fractional differential equations with mixing the Caputo derivatives and ordinary derivative.…”

Section: Introductionmentioning

confidence: 99%

Existence of Positive Solutions to Boundary Value Problems with Mixed Riemann–Liouville and Quantum Fractional Derivatives

Nyamoradi,

Ntouyas,

Tariboon

2023

Fractal Fract

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Existence and uniqueness results for mixed derivative involving fractional operators

Cited by 6 publications

References 19 publications

Analyzing a SEIR-Type Mathematical Model of SARS-COVID-19 Using Piecewise Fractional Order Operators

Analyzing a SEIR-Type Mathematical Model of SARS-COVID-19 Using Piecewise Fractional Order Operators

Study of Rotavirus Mathematical Model Using Stochastic and Piecewise Fractional Differential Operators

Existence of Positive Solutions to Boundary Value Problems with Mixed Riemann–Liouville and Quantum Fractional Derivatives

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