Search Results - "Topics in Special Functions and q-Special Functions: Theory"

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series by Ali, Khalid K., Abd El Salam, Mohamed A., Mohamed, Emad M. H., Samet, Bessem, Kumar, Sunil, Osman, M. S.

“…In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear…”
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On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals by Rahman, Gauhar, Nisar, Kottakkaran Sooppy, Ghanbari, Behzad, Abdeljawad, Thabet

“…In this paper, we establish the generalized Riemann–Liouville (RL) fractional integrals in the sense of another increasing, positive, monotone, and measurable…”
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A fractional derivative with two singular kernels and application to a heat conduction problem by Baleanu, Dumitru, Jleli, Mohamed, Kumar, Sunil, Samet, Bessem

“…In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established…”
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New estimates considering the generalized proportional Hadamard fractional integral operators by Zhou, Shuang-Shuang, Rashid, Saima, Jarad, Fahd, Kalsoom, Humaira, Chu, Yu-Ming

“…In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several…”
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A new bound for the Jensen gap pertaining twice differentiable functions with applications by Khan, Shahid, Adil Khan, Muhammad, Butt, Saad Ihsan, Chu, Yu-Ming

“…In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as…”
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Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials by Kim, Taekyun, Kim, Dae San, Kwon, Jongkyum, Lee, Hyunseok

“…The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli…”
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Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations by Bedi, Pallavi, Kumar, Anoop, Abdeljawad, Thabet, Khan, Aziz

“…In this paper, we investigate the existence of mild solutions for neutral Hilfer fractional evolution equations with noninstantaneous impulsive conditions in a…”
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Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators by Mohiuddine, S. A.

“…We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the…”
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Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters by Maqsood, Sidra, Abbas, Muhammad, Miura, Kenjiro T., Majeed, Abdul, Iqbal, Azhar

“…A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new…”
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Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation by Iqbal, Muhammad Kashif, Abbas, Muhammad, Nazir, Tahir, Ali, Nouman

“…A spline is a piecewise defined special function that is usually comprised of polynomials of a certain degree. These polynomials are supposed to generate a…”
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Some fractional calculus findings associated with the incomplete I-functions by Jangid, Kamlesh, Bhatter, Sanjay, Meena, Sapna, Baleanu, Dumitru, Al Qurashi, Maysaa, Purohit, Sunil Dutt

“…In this article, several interesting properties of the incomplete I -functions associated with the Marichev–Saigo–Maeda (MSM) fractional operators are studied…”
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Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation by Khater, Mostafa M. A., Park, Choonkil, Lee, Jung Rye, Mohamed, Mohamed S., Attia, Raghda A. M.

“…The accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J…”
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Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function by Alotaibi, Abdullah, Özger, Faruk, Mohiuddine, S. A., Alghamdi, Mohammed A.

“…In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in [ 0 , 1 ] as well as ρ > 0 and study some useful basic…”
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Novel finite point approach for solving time-fractional convection-dominated diffusion equations by Liu, Xiaomin, Abbas, Muhammad, Yang, Honghong, Qin, Xinqiang, Nazir, Tahir

“…In this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with…”
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Some results on degenerate Daehee and Bernoulli numbers and polynomials by Kim, Taekyun, Kim, Dae San, Kim, Han Young, Kwon, Jongkyum

“…In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were actually…”
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Fractional calculus operators with Appell function kernels applied to Srivastava polynomials and extended Mittag-Leffler function by Nisar, Kottakkaran Sooppy, Suthar, D. L., Agarwal, R., Purohit, S. D.

“…This article aims to establish certain image formulas associated with the fractional calculus operators with Appell function in the kernel and Caputo-type…”
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Estimates of quantum bounds pertaining to new q-integral identity with applications by Awan, Muhammad Uzair, Talib, Sadia, Kashuri, Artion, Noor, Muhammad Aslam, Chu, Yu-Ming

“…In this article, we establish a new generalized q -integral identity involving a q -differentiable function. Using this new auxiliary result, we obtain some…”
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The q-Sumudu transform and its certain properties in a generalized q-calculus theory by Al-Omari, Shrideh Khalaf

“…In this paper we consider a generalization to the q -calculus theory in the space of q -integrable functions. We introduce q -delta sequences and develop q…”
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On the weighted fractional integral inequalities for Chebyshev functionals by Rahman, Gauhar, Nisar, Kottakkaran Sooppy, Khan, Sami Ullah, Baleanu, Dumitru, Vijayakumar, V.

“…The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev’s functionals by utilizing a…”
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Blending type approximation by τ-Baskakov-Durrmeyer type hybrid operators by Mohiuddine, S. A., Kajla, Arun, Mursaleen, M., Alghamdi, Mohammed A.

“…In this work, we construct a Durrmeyer type modification of the τ -Baskakov operators depends on two parameters α > 0 and τ ∈ [ 0 , 1 ] . We derive the rate of…”
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