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 function Ψ…”
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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…”
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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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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…”
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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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Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations by Bedi, Pallavi, Kumar, Anoop, Abdeljawad, Thabet, Khan, Aziz

“… We obtain the existence results by applying the theory of resolvent operator functions, Hausdorff measure of noncompactness…”
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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…”
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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…”
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Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators by Mohiuddine, S. A.

“… for Bögel differentiable function of our GBS operators is presented…”
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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 fractional differential operators involving…”
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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…”
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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…”
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An extension of beta function, its statistical distribution, and associated fractional operator by Chandola, Ankita, Mishra Pandey, Rupakshi, Agarwal, Ritu, Dutt Purohit, Sunil

“…Recently, various forms of extended beta function have been proposed and presented by many researchers…”
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A new generalization of Mittag-Leffler function via q-calculus by Nadeem, Raghib, Usman, Talha, Nisar, Kottakkaran Sooppy, Abdeljawad, Thabet

“…The present paper deals with a new different generalization of the Mittag-Leffler function through q -calculus…”
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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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Monotonicity properties for a ratio of finite many gamma functions by Qi, Feng, Lim, Dongkyu

“…In the paper, the authors consider a ratio of finite many gamma functions and find its monotonicity properties such as complete monotonicity, the Bernstein…”
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Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions by Meena, Sapna, Bhatter, Sanjay, Jangid, Kamlesh, Purohit, Sunil Dutt

“…In this paper, we assess an integral containing incomplete H -functions and utilize it to build up an expansion formula for the incomplete H -functions including the Bessel function…”
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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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