Fractional Gauss hypergeometric differential equation

Hammad, Ma’mon Abu; Alzaareer, Hamza; Al-Zoubi, Hassan; Dutta, Hemen

doi:10.1080/09720502.2019.1706838

Cited by 11 publications

(9 citation statements)

References 7 publications

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“…In the present paper, we intend to continue the work of Abu Hammad et al [19] by finding the solutions of CFGHE about the fractional regular singular points x = 1 and x = ∞. Afterward, we give a wide study on the CFGHF as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, as a conformable fractional derivative introduced of [21], the authors in [19] used the new concept of fractional regular singular points with the technique of fractional power series to solve the CFGHDE about x = 0. They also introduced the form of the conformable fractional derivative and the integral representation of the fractional Gaussian function.…”

Section: Introductionmentioning

confidence: 99%

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Further study on the conformable fractional Gauss hypergeometric function

Abul-Ez¹,

Zayed²,

Youssef³

2020

Preprint

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This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular points x = 1 and x = ∞. Next, various generating functions of the CFGHF are established. We also develop some differential forms for the CFGHF. Subsequently, differential operators and the contiguous relations are reported. Furthermore, we introduce the conformable fractional integral representation and the fractional Laplace transform of CFGHF. As an application, and after making a suitable change of the independent variable, we provide general solutions of some known conformable fractional differential equations, which could be written by means of the CFGHF.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Further study on the conformable fractional Gauss hypergeometric function

Abul-Ez¹,

Zayed²,

Youssef³

2020

Preprint

View full text Add to dashboard Cite

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“…Furthermore, many research studies have been conducted on the theoretical and practical elements of conformable differential equations shortly after the proposition of this new definition [5,7,12,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Conformable derivative has also been applied in modeling and investigating phenomena in applied sciences and engineering [12] such as the nonlinear Boussinesq equation's travelling wave solutions [36], the coupled nonlinear Schrödinger equations [34] and regularized long wave Burgers equation [35] deterministic and stochastics forms, the approximate long water wave equation's exact solutions [37], the (1 + 3)-Zakharov-Kuznetsov equation with power-law nonlinearity analytical and numerical solutions [38], the (2 + 1)-dimensional Zoomeron equation [39,40] and 3 rd -order modified KdV equation analytical solutions [39], and the exact solutions for Whitham-Broer-Kaup equation's three various models in shallow water [41].…”

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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“…In [8], the conformable version of Euler's Theorem on homogeneous is introduced. Furthermore, in a short time, various research studies have been conducted on the theory and applications of fractional differential equations in the context of this newly introduced fractional derivative [9][10][11][12][13][14][15][16][17][18]23,24].…”

Section: Introductionmentioning

confidence: 99%

Note on the conformable boundary value problems: Sturm’s theorems and Green’s function

Martínez

Kaabar³

et al. 2021

Rev. Mex. Fís.

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Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

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Fractional Gauss hypergeometric differential equation

Cited by 11 publications

References 7 publications

Further study on the conformable fractional Gauss hypergeometric function

Further study on the conformable fractional Gauss hypergeometric function

Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

Note on the conformable boundary value problems: Sturm’s theorems and Green’s function

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