Some Results for Laplace-Type Integral Operator in Quantum Calculus
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Abstract
In the present article, we wish to discuss q-analogues of Laplace-type integrals on diverse types of q-special functions involving Fox's H-q-functions. Some of the discussed functions are the q-Bessel functions of the first kind, the q-Bessel functions of the second kind, the q-Bessel functions of the third kind, and the q-Struve functions as well. Also, we obtain some associated results related to q-analogues of the Laplace-type integral on hyperbolic sine (cosine) functions and some others of exponential order type as an application to the given theory.
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Al-Omari, Shrideh/0000-0001-8955-5552
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Keywords
J(V)(X, Q) Function, Y-V(X, K-V(X, H-V(X, Laplace-Type Integral, Y<sub>v</sub>(x, K<sub>v</sub>(x, J<sub>v</sub>(x, H<sub>v</sub>(x, H v ( x ; q ) $H_{v}(x;q)$ function, Laplace transform, Orthogonal polynomials, Arithmetic of Multiple Zeta Values and Related Functions, Y v ( x ; q ) $Y_{v}(x;q)$ function, Exponential type, Convex Functions, Operator (biology), Matrix Inequalities and Geometric Means, Mathematical analysis, Biochemistry, Gene, Orthogonal Polynomials, Gegenbauer polynomials, Differential equation, J v ( x ; q ) $J_{v}(x;q)$ function, QA1-939, FOS: Mathematics, Bessel polynomials, Bessel function, Biology, Laplace-type integral, Struve function, Algebra and Number Theory, Ecology, Applied Mathematics, Classical orthogonal polynomials, Pure mathematics, Chemistry, K v ( x ; q ) $K_{v}(x;q)$ function, FOS: Biological sciences, Physical Sciences, Repressor, Transcription factor, Type (biology), Mathematics, Ordinary differential equation, \(J_{v}(x, q)\) function, \(q\)-gamma functions, \(q\)-beta functions and integrals, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Basic hypergeometric integrals and functions defined by them, Integral operators, \(Y_{v}(x, Discrete operational calculus, \(K_{v}(x, \(H_{v}(x, \(q\)-calculus and related topics
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Citation
Al-Omari, Shrideh K. Q.; Baleanu, Dumitru; Purohit, Sunil D., "Some results for Laplace-type integral operator in quantum calculus", Advances in Difference Equations, (April 2018).
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19
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2018
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1
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