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Article
Mathematics, Applied
Amin Jajarmi et al.
Summary: Research on immunogenic tumor dynamics based on a fractional model involves investigating stability, equilibrium points, and implementing a modified predictor-corrector method. Results show the new model provides flexibility in adjusting complex dynamics and implementing a tracking control method can decrease tumor-cell population development. The satisfaction of control purpose is confirmed by simulation results tracking tumor-free steady state in realistic cases.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Ankit Kumar et al.
Summary: This paper establishes sufficient conditions for the exact controllability of the nonlocal Hilfer fractional integro-differential system of Sobolev-type using the theory of propagation family generated by the operators A and R. The main tools applied in the analysis are the theory of measure of noncompactness, fractional calculus, and Sadovskii's fixed point theorem. An example is provided to show the application of the main result.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2022)
Article
Abdullahi Yusuf et al.
International Journal of Applied and Computational Mathematics
(2022)
Article
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Kottakkaran Sooppy Nisar et al.
Summary: The ongoing study explores various solutions for the biological population model using a novel beta-time derivative operator. The soliton solutions obtained through the extended Sinh-Gordon equation expansion method and the Expa function method suggest that these methods broaden the range of solutions for fractional differential equations. Additionally, numerical simulations provide physical explanations for selected results.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Multidisciplinary
Ebenezer Bonyah et al.
Summary: Listeriosis is a zoonotic disease that affects many Sub-Saharan countries, and a mathematical model incorporating fractal-fractional orders has been developed in this paper to investigate the disease's future behaviors. The study reveals that numerical schemes are effective for predicting and analyzing complex phenomena, providing insights into the disease's spread and steady states.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Multidisciplinary
D. Baleanu et al.
Summary: A generalized fractional model is introduced to study the COVID-19 pandemic, incorporating real clinical observations for parameter estimation and simulation. The model shows better fitting to real data and provides key parameters to assess societal health conditions.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Multidisciplinary
Jagdev Singh et al.
Summary: The principal aim of this paper is to study the approximate solution of the nonlinear Caudrey-Dodd-Gibbon equation of fractional order using an analytical method. The uniqueness and convergence analysis for the method are proven. The results demonstrate that the applied technique is very efficient in obtaining solutions for fractional order mathematical models.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Multidisciplinary
Yong-Ki Ma et al.
Summary: This manuscript discusses the approximate controllability results of Hilfer fractional differential inclusions in Hilbert space and proves the approximate controllability of Hilfer fractional neutral differential inclusions using Bohnenblust-Karlin's fixed point theorem. Furthermore, nonlocal conditions are extended to the existence results, and an application is presented to demonstrate the practicality of the theoretical conclusions.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Materials Science, Multidisciplinary
Haleh Tajadodi et al.
Summary: This article discusses how to formulate exact solutions of the time fractional DBM equation, Sinh-Gordon equation and Liouville equation using the simplest equation method in the context of conformable fractional derivatives. By transforming the original equations into nonlinear ODEs, the method provides a simple yet effective approach for solving FOPDEs.
RESULTS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Aziz Khan et al.
Summary: This article investigates the existence of results and stability analysis for a nabla discrete ABC-fractional order COVID-19 model, and provides an illustrative example for its application. The study finds that the nabla discrete ABC-fractional operator is more general and applicable in modeling dynamical problems, although certain conditions are needed to ensure the proofs of existence and uniqueness theorems, as well as Hyers-Ulam stability.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Hasib Khan et al.
Summary: In this article, the fractional-order COVID-19 model is studied for analytical and computational aspects. The computational study shows that the spread will continue for a long time and recovery reduces the infection rate. The numerical scheme is based on Lagrange's interpolation polynomial and the results are similar to the integer order, demonstrating the applicability of the numerical scheme and effectiveness of the fractional order derivative.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sania Qureshi et al.
Summary: A new epidemiological model considering both integer and fractional order operators was developed to study the transmission dynamics of measles. Stability analysis and parameter sensitivity were discussed, with optimization of the fractional order parameter chi. Various simulations were conducted to observe the effects of parameters on the dynamics of the epidemic.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Kottakkaran Sooppy Nisar et al.
Summary: This article presents the controllability results of the non-dense Hilfer neutral fractional derivative using semigroup theory, fractional calculus, Banach contraction principle, and Minch technique. A numerical analysis is also provided for model enhancement.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Materials Science, Multidisciplinary
A. Jajarmi et al.
Summary: In this study, a new fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. By constructing Euler-Lagrange equations and using matrix approximation technique, a nonlinear algebraic system is derived and solved numerically, revealing various features different from previous mathematical formalism.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Pallavi Bedi et al.
Summary: This article aims to establish the controllability results for fractional differential equations of neutral type with Atangana-Baleanu-Caputo derivatives using the theory of semigroup operators and fixed point theorem coupled with a measure of noncompactness. An example is provided to verify the applicability of the obtained results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Sania Qureshi et al.
Summary: The study investigates the logistic growth model in population dynamics using both classical and non-classical differential operators with actual statistical data. The results suggest the superiority of the fractional conformable logistic model, which is explored for uniqueness through fixed point theory. Numerical simulations using the Adams iterative technique illustrate the model's behavior and provide a statistical summary of the operators.
Article
Engineering, Multidisciplinary
Amita Devi et al.
Summary: This article discusses fractional Langevin equations with Caputo Hadamard-derivative, involving non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness of solutions are defined using the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is provided to facilitate the understanding of the hypothetical outcomes.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Engineering, Multidisciplinary
Pallavi Bedi et al.
Summary: This paper discusses the controllability and stability of Hilfer fractional evolution equations in a Banach space, demonstrating the nature and uniqueness of the equations and their solutions, and obtaining results of existence and uniqueness through propagation family theory, non-compactness calculation methods, and fixed point technique. An example is provided to illustrate the main results.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Physics, Multidisciplinary
V. S. Erturk et al.
Summary: The aim of this research is to investigate the motion of a beam on an internally bent nanowire using fractional calculus theory. The study finds that fractional responses approach classical ones as the fractional order approaches unity, indicating that the fractional Euler-Lagrange equation provides more information for evaluating hidden features of the real system under investigation.
ACTA PHYSICA POLONICA A
(2021)
Article
Mathematics, Applied
Kasthurisamy Jothimani et al.
Summary: This work establishes the controllability of nondense fractional neutral delay differential equation under Hille-Yosida condition in Banach space, deriving outcomes with the aid of fractional calculus theory, semigroup operator theory, and Schauder fixed point theorem, and verifying theoretical results through illustration.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2021)
Article
Mathematics, Applied
Yong Zhou et al.
Summary: This paper discusses interesting results of mild solutions to fractional evolution systems with order alpha in the interval (1, 2) in Banach spaces, as well as the controllability problem. A new representation of solution operators and concept of mild solutions is derived using Laplace transform and Mainardi's Wright-type function. Additionally, a new compact result of solution operators is established for compact sine families. Controllability results of mild solutions are also obtained, and main results are illustrated with an example.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2021)
Article
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Jingyun Lv et al.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2020)
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Min Yang et al.
ADVANCES IN DIFFERENCE EQUATIONS
(2020)
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ALEXANDRIA ENGINEERING JOURNAL
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Vikram Singh
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(2019)
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Nguyen Huy Tuan et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
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Min Yang et al.
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Zufeng Zhang et al.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2014)
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Mohammad Ali Mohebbi Ghandehari et al.
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(2013)
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K. M. Furati et al.
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(2012)
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Yong Zhou et al.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2010)
Article
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Xianlong Fu et al.
CHINESE ANNALS OF MATHEMATICS SERIES B
(2007)
Article
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EP Gatsori
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2004)
