Geometric meaning of conformable derivative via fractional cords

Khalil, Roshdi; Horani, Mohammed Al; Hammad, Ma’mon Abu

doi:10.22436/jmcs.019.04.03

Cited by 48 publications

(25 citation statements)

References 5 publications

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“…Almeida et al (2016) discussed in [8] that conformable derivative is an interesting topic of research that deserves to be studied further. In addition, both Zhao & Luo (2017) and Khalil et al (2019) presented the physical and geometrical meaning of conformable derivative in [9,10], respectively. Tuan et al [11] investigated the mild solutions' existence and regularity of the proposed initial value problem for time diffusion equation in the sense of conformable derivative.…”

Section: Introductionmentioning

confidence: 99%

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

Martínez

Kaabar

et al. 2021

Journal of Mathematics

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The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable formula of finite increments.

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Section: Introductionmentioning

confidence: 99%

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

Martínez

Kaabar

et al. 2021

Journal of Mathematics

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“…Modeling real-life problems with conformable derivatives ( [19], [20]). Other fractional derivatives do not have geometrical interpretation but conformable derivative has [21]. For relevant concepts on conformable calculus, see for example ( [22], [23], [24]).…”

Section: Introductionmentioning

confidence: 99%

Some Fundamental Results on Fuzzy Conformable Differential Calculus

Younus¹,

Asif²,

Atta³

et al. 2021

J Frac Calc & Nonlinear Sys

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In this paper, we combine fuzzy calculus, and conformable calculus to introduce the fuzzy conformable calculus. We define the fuzzy conformable derivative of order $2\Psi $ and generalize it to derivatives of order $p\Psi $. Several properties on difference, product, sum, and addition of two fuzzy-valued functions are provided which are used in the solution of the fuzzy conformable differential equations. Also, examples in each case are given to illustrate the utility of our results.

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“…This new definition differs from other fractional derivatives and is similar to the classical one. Fractional derivatives have no geometrical interpretation because of their non-local behavior but conformable derivative inherits the local behavior of the usual derivative and possesses the geometrical interpretation [14].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Fuzzy Linear Differential Equations in the Conformable Setting

Younus¹,

Asif²,

Atta³

et al. 2021

J Frac Calc & Nonlinear Sys

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In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.

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Geometric meaning of conformable derivative via fractional cords

Cited by 48 publications

References 5 publications

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

Some Fundamental Results on Fuzzy Conformable Differential Calculus

Analytical Solutions of Fuzzy Linear Differential Equations in the Conformable Setting

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