Dynamic cobweb models with conformable fractional derivatives

Böhner, Martin; Hatipoğlu, Veysel Fuat

doi:10.1016/j.nahs.2018.09.004

Cited by 46 publications

(21 citation statements)

References 6 publications

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“…Further development on conformable fractional derivative and its applications on arbitrary time scales can be seen through the articles [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A new conformable nabla derivative and its application on arbitrary time scales

Rahmat

Noorani

2021

Adv Differ Equ

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In this article, we introduce a new type of conformable derivative and integral which involve the time scale power function $\widehat{\mathcal{G}}_{\eta }(t, a)$ G ˆ η ( t , a ) for $t,a\in \mathbb{T}$ t , a ∈ T . The time scale power function takes the form $(t-a)^{\eta }$ ( t − a ) η for $\mathbb{T}=\mathbb{R}$ T = R which reduces to the definition of conformable fractional derivative defined by Khalil et al. (2014). For the discrete time scales, it is completely novel, where the power function takes the form $(t-a)^{(\eta )}$ ( t − a ) ( η ) which is an increasing factorial function suitable for discrete time scales analysis. We introduce a new conformable exponential function and study its properties. Finally, we consider the conformable dynamic equation of the form $\bigtriangledown _{a}^{\gamma }y(t)=y(t, f(t))$ ▽ a γ y ( t ) = y ( t , f ( t ) ) , and study the existence and uniqueness of the solution. As an application, we show that the conformable exponential function is the unique solution to the given dynamic equation. We also examine the analogue of Gronwall’s inequality and its application on time scales.

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“…Further development on conformable fractional derivative and its applications on arbitrary time scales can be seen through the articles [24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A new conformable nabla derivative and its application on arbitrary time scales

Rahmat

Noorani

2021

Adv Differ Equ

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“…Recently, researchers have started to deal with studies relating to conformable calculus on time scales (see [10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Spectral Properties of a Conformable Boundary Value Problem on Time Scales

Ceylan

2021

Journal of Universal Mathematics

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We study a self-adjoint conformable dynamic equation of second order on an arbitrary time scale T. We state an existence and uniqueness theorem for the solutions of this equation. We prove the conformable Lagrange identity on time scales. Then, we consider a conformable eigenvalue problem generated by the above-mentioned dynamic equation of second order and we examine some of the spectral properties of this boundary value problem.

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“…The conformable derivative can be regarded as a natural extension of the classical differential operator, which satisfies most important properties, such as the chain rule [29][30][31]. Researchers have recently applied conformable derivatives to many scientific fields [32][33][34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

et al. 2019

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A new chaotic financial system is proposed by considering ethics involvement in a fourdimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integerorder system. A discretization scheme is proposed to calculate numerical solutions of conformable derivative systems. The scheme is illustrated by testing hyperchaos for the system. among interest rates, investments, prices, and savings. Chen [12] presented a fractional form of nonlinear financial system. Wang, Huang and Shen [13] established an uncertain fractional-order form of the financial system. Mircea et al. [14] set up a delayed form of the financial system. Xin, Chen, and Ma [15] proposed a discrete form of financial system. Yu, Cai, and Li [16] extended the

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Dynamic cobweb models with conformable fractional derivatives

Cited by 46 publications

References 6 publications

A new conformable nabla derivative and its application on arbitrary time scales

A new conformable nabla derivative and its application on arbitrary time scales

Spectral Properties of a Conformable Boundary Value Problem on Time Scales

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

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