The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the V-Function by S. Chandak, Biniyam Shimelis, Nigussie Abeye, A. Padma

“…In addition, on account of V-function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.…”
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On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions by Muajebah Hidan, Mohamed Akel, Salah Mahmoud Boulaaras, Mohamed Abdalla

“…Recently, the applications and importance of integral transforms (or operators) with special functions and polynomials have received more attention in various fields like fractional analysis, survival analysis, physics, statistics, and engendering. …”
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Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds by Shenyang Tan, Tiren Huang, Wenbin Zhang

“…We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere.…”
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On monomiality property of q-Gould-Hopper-Appell polynomials by Nusrat Raza, Mohammed Fadel, Subuhi Khan

“…Recently, in the theory of q-special functions, the extension of the monomiality concept to q-special polynomials is introduced. …”
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Structural transitions in a NiTi alloy: a multistage loading-unload cycle by V. Di Cocco, C. Maletta, S. Natali

“…NiTi shape memory alloys (SMAs) are increasingly used in many engineering and medical applications, because they combine special functional properties, such as shape memory effect and pseudoelasticity, with good mechanical strength and biocompatibility. …”
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Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators by D. L. Suthar, Fasil Gidaf, Mitku Andualem

“…Due to the general nature of the I-function and the generalized M-series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.…”
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Functional mechanism on stem cells by tea (Camellia sinensis) bioactive compounds by Yao Cheng, Jiachen Sun, Hui Zhao, Hongxing Guo, Jianying Li

“…Stem cells (SCs) are the immature and undifferentiated cells by a varying capacity for proliferation, self-renewal and the capability to differentiate into one or more different derivatives with specialized function or maintain their stem cell phenotype. …”
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Quantum–Fractal–Fractional Operator in a Complex Domain by Adel A. Attiya, Rabha W. Ibrahim, Ali H. Hakami, Nak Eun Cho, Mansour F. Yassen

“…Some examples are considered, involving special functions like Bessel and generalized hypergeometric functions.…”
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k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications by Saad Ihsan Butt, Jamshed Nasir, Shahid Qaisar, Khadijah M. Abualnaja

“…As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.…”
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Performance analysis of antenna correlation on land mobile satellite based MIMO systems by Yuan LIN, Yuan-zhi HE, Jing-chao WANG, Han HAN

“…The joint effect of spatial correlation and shadowing of channels on the performance of land mobile satellite MIMO system was analyzed.With the help of contour integral,residue theorem and integral of special functions,closed-form approximations of the outage probability (OP) and the average symbol error rate (SER)were derived.The Monte Carlo simulations results were illustrated through several examples in order to assess the impact of correlation coefficient,the number of antenna and different modulation mode on the performance.It shows that although channel correlation and shadowing degrade system gain,significant performance gains can be obtained by multi-satellite MIMO systems compared to relevant single-input single-output (SISO) ones.…”
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Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model by Andrade, Jose A. A., Rathie, Pushpa

“…The results are based on special functions and we give exact expressions for the posterior density, moments, and cumulative distribution. …”
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Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications by Lokenath Debnath, Bicheng Yang

“…Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. …”
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Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments by Wei Li, Chang-Yuan Chen, Shi-Hai Dong

“…The present method can in principle be generalizable to the integrals involving other special functions. As an illustration we also study a typical Bessel integral with a complicated argument ∫0∞Jn(αx2+z2)/(x2+z2)nx2m+1dx.…”
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Design of Key Joint Reducer for Heavy-duty Teleoperation Manipulator by Zhou Zhenguo, Bai Xiaowei, Zhou Zibo

“…Because of the key joint of the manipulator will bear excessive load during maintenance,and the main reducer of the manipulator must have a self-locking function,and special functional requirements such as space for cable channels are reserved in the middle of the main reducer. …”
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Harmonic analysis on the quantized Riemann sphere by Jaak Peetre, Genkai Zhang

“…In the course of the discussion many special functions (hypergeometric functions, orthogonal polynomials etc.) come up. …”
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Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators by Noureddine Azzouz, Bouharket Benaissa, Hüseyin Budak, İzzettin Demir

“…Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. …”
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Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable by Najla M. Alarifi, Rabha W. Ibrahim

“…A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. …”
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Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion by Ndolane Sene

“…The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G-function. …”
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Investigation and analysis of the weakness and efficiency of generalized cycling attacks on RSA modulus by JIANG Zheng-tao1, HUAI Jin-peng2, WANG Yu-min4

“…The efficiency of attacking methods on secure RSA modulus was investigated.It was pointed out by analysis that since the success probability of some attack methods was neglectable,these methods could not be regarded as the reason for choosing strongly secure RSA modulus.In consideration of the analysis of attack methods,the signification of secure RSA modulus was summarized,which enhanced the efficiency of selecting secure parameters in practice.The result that the difference between two RSA primes d=|p-q| must not be too small was further investigated,and the d might be seen as a special case when dl,m=ql-pm（l,m∈Z+） was small.From the analysis,it could be figured out that the randomness of the relation between the two primes should not be neglected during selecting RSA modulus.To improve the security,it should be avoided to have some specially functional relations between the two primes when choosing a…”
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An effective computational approach to the local fractional low-pass electrical transmission lines model by Kang-Jia Wang

“…By defining the Mittag-Leffler function (MLF) on the Cantor set (CS), two special functions, namely, theLTδ-function and LCδ-function, are extracted to develop an auxiliary function, which is employed to look for the non-differentiable (ND) exact solutions (ESs) together with Yang’s non-differentiable transformation. …”
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