Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense

Budak, Hüseyın; Sarıkaya, Mehmet Zeki; Set, Erhan

doi:10.17512/jamcm.2016.4.02

Cited by 18 publications

(6 citation statements)

References 15 publications

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“…[1][2][3][4][5][6][7][8] The theory of the local fractional derivative (LFD) is a mathematical tool for describing fractals, that was used to model the fractal complexity in shallow water surfaces, 14 LC-electric circuit, 15 traveling-wave solution of the Burgerstype equation, 16 PDEs, [17][18][19][20] ODEs, 21 and inequalities. 22,23 The useful models for the LFD were considered [24][25][26][27][28][29] and discussed. 30 However, the nonlinear local fractional Boussinesq equations and their non-differentiable-type traveling-wave solutions have not yet been tackled.…”

Section: Introductionmentioning

confidence: 99%

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

2017

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The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable ¶ Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. X. -J. Yang, J. A. T. Machado & D. Baleanu graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains. 1740006-1

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Section: Introductionmentioning

confidence: 99%

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

2017

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“…. For more results related to the generalized s-convex in the second sense on fractal sets , the interested reader is directed to [66] and [16].…”

Section: As Hudzik and Maligranda Mentioned That The Conditionmentioning

confidence: 99%

“…The constant 1 s+1 is best possible in the second part of inequality (16). We refer the reader to [88] and [53] for more results connected to H-H type inequalities via s-convex in the second sense.…”

Section: H-h Type Inequalities For Various Classes Of Convexitiesmentioning

confidence: 99%

A Systematic Review on Hermite-Hadamard Inequality: Theory and Applications

Almutairi¹,

Kılıçman²

2021

Preprint

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Inequalities play important roles not only in mathematics, but also in other fields, such as economics and engineering. Even though many results are published on Hermite-Hadamard (H-H) type inequalities, new researcher to this fields often found it difficult to understand them. Thus, some important discoverers, such as the formulations of H-H type inequalities via various classes of convexity, through differentiable mappings and for fractional integrals, are presented. Some well-known examples from previous literature are used as illustrations.

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“…For several Ostrowski type inequalities for Riemann-Liouville fractional integrals see [1]- [5], [16]- [27] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Trapezoid type inequalities for generalized Riemann-Liouville fractional integrals of functions with bounded variation

Dragomir

2020

Acta Universitatis Sapientiae, Mathematica

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Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense

Abstract: Abstract. In this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense.

Cited by 18 publications

References 15 publications

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

A Systematic Review on Hermite-Hadamard Inequality: Theory and Applications

Trapezoid type inequalities for generalized Riemann-Liouville fractional integrals of functions with bounded variation

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