On generalization conformable fractional integral inequalities

Usta, Fuat; Zeki, Mehmet

doi:10.2298/fil1816519u

Cited by 15 publications

(16 citation statements)

References 12 publications

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“…For the convenience of the reader, we give some background from fractional calculus theory. These materials can be found in the recent literature, see [12,13,23].…”

Section: Conformable Fractional Calculusmentioning

confidence: 99%

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Oscillation theorems for three classes of conformable fractional differential equations

Lü

Sun

2019

Adv Differ Equ

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In this paper, we consider the oscillation theory for fractional differential equations. We obtain oscillation criteria for three classes of fractional differential equations of the forms T t 0 α x(t) + m i=1 p i (t)x(τ i (t)) = 0, t ≥ t 0 , T t 0 α (r(t)(T t 0 α (x(t) + p(t)x(τ (t)))) β) + q(t)x β (σ (t)) = 0, t ≥ t 0 , and T t 0 α (r 2 T t 0 α (r 1 (T t 0 α y) β))(t) + p(t)(T t 0 α y(t)) β + q(t)f (y(g(t))) = 0, t ≥ t 0 , where T α denotes the conformable differential operator of order α, 0 < α ≤ 1.

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“…For the convenience of the reader, we give some background from fractional calculus theory. These materials can be found in the recent literature, see [12,13,23].…”

Section: Conformable Fractional Calculusmentioning

confidence: 99%

“…This new theory is improved by Abdeljawad [13]. For recent results on conformable fractional derivatives, we refer the reader to [14][15][16][17][18][19][20][21][22][23]. This new definition satisfies formulas of the derivatives of the product and quotient of two functions and has a simpler chain rule.…”

Section: Introductionmentioning

confidence: 99%

Oscillation theorems for three classes of conformable fractional differential equations

Lü

Sun

2019

Adv Differ Equ

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“…Equation (20) is a nonlinear fractional ordinary differential equation with con- (20) to an equivalent form…”

Section: Lie Symmetry Analysis Of Cfpdesmentioning

confidence: 99%

Lie symmetry analysis of some conformable fractional partial differential equations

Tayyan

Sakka

2018

Arab. J. Math.

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In this article, Lie symmetry analysis is used to investigate invariance properties of some nonlinear fractional partial differential equations with conformable fractional time and space derivatives. The analysis is applied to Korteweg-de Vries, modified Korteweg-de Vries, Burgers, and modified Burgers equations with conformable fractional time and space derivatives. For each equation, all of the vector fields and the Lie symmetries are obtained. Moreover, exact solutions are given to these equations in terms of solutions of ordinary differential equations. In particular, it is shown that the fractional Korteweg-de Vries can be reduced to the first Painlevé equation and to fractional second Painlevé equation. In addition a solution of the fractional modified Korteweg-de Vries is given in terms of solutions of fractional second Painlevé equation.

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“…The conformable derivative is a local derivative which has a physical and a geometrical interpretations and potential applications in physics and engineering [7,8]. It satisfies the nice properties of the integer derivative such as, the product rule, the quotient rule, and the chain rule, and it holds that…”

Section: Introductionmentioning

confidence: 99%

The Fractional Laguerre Equation: Series Solutions and Fractional Laguerre Functions

Shat

Al-Refai

Alhamayda

et al. 2019

Front. Appl. Math. Stat.

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In this paper, we propose a fractional generalization of the well-known Laguerre differential equation. We replace the integer derivative by the conformable derivative of order 0 < α < 1. We then apply the Frobenius method with the fractional power series expansion to obtain two linearly independent solutions of the problem. For certain eigenvalues, the infinite series solution truncate to obtain the singular and non-singular fractional Laguerre functions. We obtain the fractional Laguerre functions in closed forms, and establish their orthogonality result. The applicability of the new fractional Laguerre functions is illustrated.

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On generalization conformable fractional integral inequalities

Cited by 15 publications

References 12 publications

Oscillation theorems for three classes of conformable fractional differential equations

Oscillation theorems for three classes of conformable fractional differential equations

Lie symmetry analysis of some conformable fractional partial differential equations

The Fractional Laguerre Equation: Series Solutions and Fractional Laguerre Functions

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