New Expansion Formulas for a Family of the λ-Generalized Hurwitz-Lerch Zeta Functions by H. M. Srivastava, Sébastien Gaboury

“…These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. …”
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Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes by Abdon Atangana, Dumitru Baleanu

“…A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. …”
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On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative by Ali El Mfadel, Said Melliani, M’hamed Elomari

“…The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. …”
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Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach by Zhi-Yong Chen, Carlo Cattani, Wei-Ping Zhong

“…Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.…”
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Almost Periodic Functions on Time Scales and Applications by Yongkun Li, Chao Wang

“…We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. …”
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering by Taekyun Kim, Dae San Kim, Hye Kyung Kim

“…Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators. …”
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Robot-Assisted Removal of a Partially Intravesical Intrauterine Device (IUD) and Large Bladder Stone by Cassandra Heaney, Paul Lee, Andrew Winer

“…We present a case report of a 41-year-old woman who was found to have a partially intravesical IUD and associated 2.4 cm bladder calculus. Removal of the intravesical IUD and stone was achieved with cystoscopy, cystolitholapaxy, and robot-assisted laparoscopic cystotomy.…”
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Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term by S. Manikandan, V. Muthulakshmi, S. Harikrishnan, Porpattama Hammachukiattikul

“…Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. Also, we extend the study of oscillation to conformable fractional Euler-type dynamic equation. …”
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On the finite Fourier transforms of functions with infinite discontinuities by Branko Saric

“…The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. …”
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Fractional Order Models of Industrial Pneumatic Controllers by Abolhassan Razminia, Dumitru Baleanu

“…In the light of fractional calculus, a fractional order derivative-derivative (FrDD) controller and integral-derivative (FrID) are remodeled. …”
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Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String by Ming-Sheng Hu, Ravi P. Agarwal, Xiao-Jun Yang

“…We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. …”
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Multivariate Dynamic Sneak-Out Inequalities on Time Scales by Ammara Nosheen, Aneeqa Aslam, Khuram Ali Khan, Khalid Mahmood Awan, Hamid Reza Moradi

“…In seeking applications, these inequalities are discussed in classical, discrete, and quantum calculus.…”
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The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations by W. K. Zahra, S. M. Elkholy

“…Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. …”
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Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems by Junhai Luo, Heng Liu

“…The fractional order calculus is employed in the parameter updating stage. …”
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Efficient Variational Approaches for Deformable Registration of Images by Mehmet Ali Akinlar, Muhammet Kurulay, Aydin Secer, Mustafa Bayram

“…Image registration, an ill-posed optimization problem, is solved using a gradient-descent-based method and some fundamental theorems in calculus of variations. Euler-Lagrange equations with homogeneous Neumann boundary conditions are obtained. …”
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Option Pricing under the Subordinated Market Models by Longjin Lv, Changjuan Zheng, Luna Wang

“…Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. …”
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Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series by Xiang-Chao Shi, Lan-Lan Huang, Zhen-Guo Deng, Dan Liu

“…Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. …”
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Traumatic fibroma – a review by Marco Antonio Rocafuerte - Acurio

“…The traumatic fibroma is a reactive fibrous hyperplasia caused by trauma or local irritation, such as the presence of calculus, overhanging margins of restorations, orthodontic appliances, among others. …”
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Multipoint BVP for the Langevin Equation under φ-Hilfer Fractional Operator by Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad

“…At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach contraction principle. …”
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