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On fractional (p,q) $(p,q)$-calculus [PDF]

Advances in Difference Equations, 2020
In this paper, the new concepts of (p,q) $(p,q)$-difference operators are introduced. The properties of fractional (p,q) $(p,q)$-calculus in the sense of a (p,q) $(p,q)$-difference operator are introduced and developed.
Jarunee Soontharanon, Thanin Sitthiwirattham   +1 more
doaj   +4 more sources

Opial inequality in q-calculus [PDF]

Journal of Inequalities and Applications, 2018
In this article we give q-analogs of the Opial inequality for q-decreasing functions. Using a closed form of the restricted q-integral (see Gauchman in Comput. Math. Appl. 47:281–300, 2004), we establish a new integral inequality of the q-Opial type.
Tatjana Z. Mirković, Slobodan B. Tričković, Miomir S. Stanković   +2 more
doaj   +6 more sources

Some trapezoid and midpoint type inequalities via fractional ( p , q ) $(p,q)$ -calculus

Advances in Difference Equations, 2021
Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q ...
Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, Praveen Agarwal   +4 more
doaj   +2 more sources

On Some New Maclaurin’s Type Inequalities for Convex Functions in q-Calculus

Fractal and Fractional, 2023
This work establishes some new inequalities to find error bounds for Maclaurin’s formulas in the framework of q-calculus. For this, we first prove an integral identity involving q-integral and q-derivative.
Thanin Sitthiwirattham, Muhammad Aamir Ali, Hüseyin Budak   +2 more
doaj   +2 more sources

On q-Calculus and Starlike Functions [PDF]

Boletín de la Sociedad Matemática Mexicana, 2019
We consider the class S∗(ζ,α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin ...
K. Piejko, J. Sokół, K. Tra̧bka-Wiȩcław   +2 more
semanticscholar   +3 more sources

On convolution and q-calculus [PDF]

Iranian Journal of Science and Technology, Transactions A: Science, 2019
We consider the convolution operator dζf(z)=1zf(z)∗z(1-ζz)(1-z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
K. Piejko, J. Sokół
semanticscholar   +2 more sources

On modified Dunkl generalization of Szász operators via q-calculus. [PDF]

J Inequal Appl, 2017
الغرض من هذه الورقة هو إدخال تعديل على تعميم q - Dunkl للدوال الأسية. تتيح هذه الأنواع من العوامل تقديرًا أفضل للأخطاء على الفاصل الزمني $[\frac{1 }{ 2},\infty )$ من الأنواع الكلاسيكية. نحصل على بعض النتائج التقريبية من خلال نظرية معروفة من نوع كوروفكين ونظرية مرجحة من نوع كوروفكين. علاوة على ذلك، نحصل على معدل تقارب المشغلين للوظائف التي تنتمي إلى فئة
Mursaleen M, Nasiruzzaman M, Alotaibi A.
europepmc   +6 more sources

Some Opial-type integral inequalities via (p,q) $(p,q)$-calculus

Journal of Inequalities and Applications, 2019
In this paper, we introduce a new Opial-type inequality by using (p,q) $(p,q)$-calculus and establish some integral inequalities. We find a (p,q) $(p,q)$-generalization of a Steffensens-type integral inequality and some other inequalities.
Md. Nasiruzzaman, Aiman Mukheimer, M. Mursaleen   +2 more
doaj   +2 more sources

Some Carleman-type inequalities in ( p , q ) $(p,q)$ -calculus

Journal of Inequalities and Applications
In this paper, we construct ( p , q ) $\left (p,q\right )$ -type Jessen’s inequality using the properties of convex functions. On this basis, we generalize the classical Carleman integral-type inequality in ( p , q ) $\left (p,q\right )$ -calculus and ...
Jiao Yu, Lin Han
doaj   +3 more sources

On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2021
This paper is devoted to explicit and numerical solutions to linear fractional q-difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q-derivative in q-calculus.
S. Shaimardan, N.S. Tokmagambetov
doaj   +3 more sources