Analysis of New Trends of Fractional Differential Equations

Atangana, Abdon; Akgül, Ali

doi:10.1002/9781119654223.ch3

Cited by 12 publications

(3 citation statements)

References 13 publications

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“…to the memory-dependent derivative operator D m τ and using the convolution theorem, we get (Atangana and Akgul 2020;Akgul et al 2020)…”

Section: Methods Of Solutionmentioning

confidence: 99%

Memory dependent magneto-thermoelastic interaction in a rotating medium based on refined multi-phase-lag model

De,

Purkait,

Das

et al. 2024

Preprint

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This article deals with the problem of wave propagation in a two-dimensional rotating medium under the influence of magnetic field based on refined multi-phase-lag model of thermoelasticity theory with memory-dependent derivative. The classical thermoelasticity theory, Lord-Shulman theory, Green-Naghdi IItheory and simple phase lag theory may be established as special cases of the refined multi-phase-lag thermoelasticity theory. A non-Gaussian laser beam is used to heat the bounding plane surface. Laplace and Fourier transform techniques are used to generate analytical formulae for several physical quantities onthe transformed domain. Using MATHEMATICA 10, the inversion of double transform has been performed numerically. Zakian method is used for the numerical inversion of Laplace transform. In order to demonstrate the effect of rotation, magnetic field and different kernel functions on all the main quantities such as displacements,temperature and stresses, the quantities are computed numerically and presented graphically for Lord-Shulman model with memory dependent derivative.

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“…to the memory-dependent derivative operator D m τ and using the convolution theorem, we get (Atangana and Akgul 2020;Akgul et al 2020)…”

Section: Methods Of Solutionmentioning

confidence: 99%

Memory dependent magneto-thermoelastic interaction in a rotating medium based on refined multi-phase-lag model

De,

Purkait,

Das

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Mathematical modeling has a rich literature on the transmission dynamics of infectious diseases. Mathematical modeling is one of the powerful tools to describe the dynamical behavior of different diseases [22] , [23] , [24] , [25] , [26] , [27] .…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan)

et al. 2021

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“…The existence, uniqueness, and global behavior of solutions for boundary value problems of fractional differential equations have been considered in several recent papers (see, e.g., [1,[4][5][6][7][8][9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

2021

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We deal with the following Riemann–Liouville fractional nonlinear boundary value problem: $$ \textstyle\begin{cases} \mathcal{D}^{\alpha }v(x)+f(x,v(x))=0, & 2< \alpha \leq 3, x\in (0,1), \\ v(0)=v^{\prime }(0)=v(1)=0. \end{cases} $$ { D α v ( x ) + f ( x , v ( x ) ) = 0 , 2 < α ≤ 3 , x ∈ ( 0 , 1 ) , v ( 0 ) = v ′ ( 0 ) = v ( 1 ) = 0 . Under mild assumptions, we prove the existence of a unique continuous solution v to this problem satisfying $$ \bigl\vert v(x) \bigr\vert \leq cx^{\alpha -1}(1-x)\quad\text{for all }x \in [ 0,1]\text{ and some }c>0. $$ | v ( x ) | ≤ c x α − 1 ( 1 − x ) for all x ∈ [ 0 , 1 ] and some c > 0 . Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68–73, 2017).

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Analysis of New Trends of Fractional Differential Equations

Cited by 12 publications

References 13 publications

Memory dependent magneto-thermoelastic interaction in a rotating medium based on refined multi-phase-lag model

Memory dependent magneto-thermoelastic interaction in a rotating medium based on refined multi-phase-lag model

Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan)

Existence and uniqueness of solutions for a class of fractional nonlinear boundary value problems under mild assumptions

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