A Family of the <i>r</i>-Associated Stirling Numbers of the Second Kind and Generalized Bernoulli Polynomials by Paolo Emilio Ricci, Rekha Srivastava, Pierpaolo Natalini

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Lagrange-Based Hypergeometric Bernoulli Polynomials by Sahar Albosaily, Yamilet Quintana, Azhar Iqbal, Waseem A. Khan

“…In this paper, we introduce the family of the Lagrange-based hypergeometric Bernoulli polynomials via the generating function method. …”
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Some Geometric Properties of a Family of Analytic Functions Involving a Generalized <i>q</i>-Operator by Lei Shi, Muhammad Ghaffar Khan, Bakhtiar Ahmad

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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials by Dionisio Peralta, Yamilet Quintana, Shahid Ahmad Wani

“…In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. …”
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Discrete quasiprobability distributions involving Bernoulli polynomials by Bander Almutairi

“…The aim of this short paper is to present a new family of discrete densities with two parameters based on Bernoulli numbers and polynomials. …”
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Other approaches for generalized Bernoulli–Euler polynomials and beyond by Hacène Belbachir, Slimane Hadj-Brahim, Mustapha Rachidi

“…In this paper we develop two approaches for studying a large family of generalized Bernoulli–Euler polynomials. …”
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A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function by Daeyeoul Kim, Yilmaz Simsek

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On Generalized Bivariate (<i>p</i>,<i>q</i>)-Bernoulli–Fibonacci Polynomials and Generalized Bivariate (<i>p</i>,<i>q</i>)-Bernoulli–Lucas Polynomials by Hao Guan, Waseem Ahmad Khan, Can Kızılateş

“…Finally, we provide some families of bilinear and bilateral generating functions for the generalized bivariate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Bernoulli–Fibonacci polynomials.…”
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Analytical solutions to time-space fractional Kuramoto-Sivashinsky Model using the integrated Bäcklund transformation and Riccati-Bernoulli sub-ODE method by M. Mossa Al-Sawalha, Safyan Mukhtar, Albandari W. Alrowaily, Saleh Alshammari, , Sherif. M. E. Ismaeel, S. A. El-Tantawy

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A Family of Generalized Legendre-Based Apostol-Type Polynomials by Talha Usman, Nabiullah Khan, Mohd Aman, Junesang Choi

“…The purpose of this work is to provide a unified family of Legendre-based generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-Genocchi polynomials, with appropriate constraints for the Maclaurin series. …”
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Primary resonance of an Euler-Bernoulli nano-beam modelled with second strain gradient by Hossein Mohammadi, Soroush Sepehri

“…<span style="font-family: 'Times New Roman','serif'; font-size: 10pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-bidi-font-size: 9.0pt;">In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper for the first time. …”
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Some New Families of Special Polynomials and Numbers Associated with Finite Operators by Yilmaz Simsek

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Comparison of Poisson and Bernoulli spatial cluster analyses of pediatric injuries in a fire district by Warden Craig R

“…There was some overlap in geographic clusters identified by both methods. The Bernoulli method allows more focused cluster mapping and evaluation since it directly uses location data. …”
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New families of soliton solutions for the (2 + 1)-dimensional nonlinear evolution equation arising in nonlinear optics by Khalid K. Ali, Mohamed Omri, M.S. Mehanna, Hatem Besbes, Abdel-Haleem Abdel-Aty

“…This article aims to achieve families of new traveling wave solutions to the (2 + 1)-dimensional nonlinear evolution equation using three powerful analytical techniques: the general form of Kudryashov’s method, the Bernoulli sub-ODE method, and the extended direct algebraic method. …”
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New Families of Special Polynomial Identities Based upon Combinatorial Sums Related to <i>p</i>-Adic Integrals by Yilmaz Simsek

“…Using these generating functions with their functional equation, we derive various interesting combinatorial sums and identities including new families of numbers and polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, the Changhee numbers, and other numbers and polynomials. …”
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Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions by Monireh Nosrati Sahlan, Hojjat Afshari, Jehad Alzabut, Ghada Alobaidi

“…In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. …”
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A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials by Ghulam Muhiuddin, Waseem Ahmad Khan, Ugur Duran, Deena Al-Kadi

“…The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. …”
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On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus by Can Kızılateş, Halit Öztürk

“…This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol Genocchi-Fibonacci polynomials by using Golden calculus. …”
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Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions by Yilmaz Simsek, Daeyeoul Kim

“…Relations between these new families of special numbers and polynomials and Bernoulli numbers and polynomials are given. …”
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Radius Results for Certain Strongly Starlike Functions by Afis Saliu, Kanwal Jabeen, Qin Xin, Fairouz Tchier, Sarfraz Nawaz Malik

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