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The history of qcalculus and a new method
, 2000
"... 1.1. Partitions, generalized Vandermonde determinants and representation theory. 5 1.2. The Frobenius character formulae. 8 ..."
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1.1. Partitions, generalized Vandermonde determinants and representation theory. 5 1.2. The Frobenius character formulae. 8
Nontrivial solutions for fractional qdifference boundary value problems
, 2010
"... In this paper, we investigate the existence of nontrivial solutions to the nonlinear qfractional boundary value problem (D α q y)(x) = −f(x,y(x)), 0 < x < 1, y(0) = 0 = y(1), by applying a fixed point theorem in cones. ..."
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In this paper, we investigate the existence of nontrivial solutions to the nonlinear qfractional boundary value problem (D α q y)(x) = −f(x,y(x)), 0 < x < 1, y(0) = 0 = y(1), by applying a fixed point theorem in cones.
The different tongues of qcalculus
, 2008
"... In this review paper we summarize the various dialects of qcalculus: quantum calculus, time scales, and partitions. The close connection between Γq(x) functions on the one hand, and elliptic functions and theta functions on the other hand will be shown. The advantages of the Heine notation will b ..."
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Cited by 5 (2 self)
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In this review paper we summarize the various dialects of qcalculus: quantum calculus, time scales, and partitions. The close connection between Γq(x) functions on the one hand, and elliptic functions and theta functions on the other hand will be shown. The advantages of the Heine notation will be illustrated by the (q)Euler reflection formula, qAppell functions, Carlitz– AlSalam polynomials, and the socalled qaddition. We conclude with some short biographies about famous scientists in qcalculus.
TURÁNTYPE INEQUALITIES FOR SOME qSPECIAL FUNCTIONS
, 2009
"... ABSTRACT. In this paper, we give new Turántype inequalities for some qspecial functions, using a q analogue of a generalization of the Schwarz inequality. Key words and phrases: Turan’s inequality, qpolygamma functions, qzeta function. 2000 Mathematics Subject Classification. 26D07, 26D15, 33D0 ..."
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ABSTRACT. In this paper, we give new Turántype inequalities for some qspecial functions, using a q analogue of a generalization of the Schwarz inequality. Key words and phrases: Turan’s inequality, qpolygamma functions, qzeta function. 2000 Mathematics Subject Classification. 26D07, 26D15, 33D05. 1.
Analytic continuation of solutions of the pantograph equation by means of θ modular formula, preprint ArXiv
, 2012
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UNCERTAINTY PRINCIPLES FOR THE FOURIER TRANSFORMS IN QUANTUM CALCULUS
, 2006
"... Abstract. Some properties of the qFouriersine transform are studied and qanalogues of the Heisenberg uncertainty principle is derived for the qFouriercosine transform studied in [5] and for the qFouriersine transform. 1. ..."
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Abstract. Some properties of the qFouriersine transform are studied and qanalogues of the Heisenberg uncertainty principle is derived for the qFouriercosine transform studied in [5] and for the qFouriersine transform. 1.
study on a new fractional integral inequality in quantum calculus
 Advanced Studies inTheoretical Physics
, 2013
"... Abstract In this paper, we present a new fractional integral inequality in quantum calculus. Mathematics Subject Classification: 26D10, 26D15 ..."
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Abstract In this paper, we present a new fractional integral inequality in quantum calculus. Mathematics Subject Classification: 26D10, 26D15
Wavelet Transforms in Quantum Calculus
, 2005
"... This paper aims to study the qwavelets and the qwavelet transforms, using only the qJackson integrals and the qcosine Fourier transform, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical theory by giving their qanalogues. 1 ..."
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This paper aims to study the qwavelets and the qwavelet transforms, using only the qJackson integrals and the qcosine Fourier transform, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical theory by giving their qanalogues. 1