Periodically Kicked Rotator with Power-Law Memory: Exact Solution and Discrete Maps by Vasily E. Tarasov

“…This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. …”
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Fractional Critical Damping Theory and Its Application in Active Suspension Control by Peng Wang, Qingyun Wang, Xiaomei Xu, Ning Chen

“…Based on the principle of modal coordinate transformation, a new design method of fractional skyhook damping control for full-car suspension is given. …”
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Computational Approach for Differential Equations with Local and Nonlocal Fractional-Order Differential Operators by null Kamran, Ujala Gul, Fahad M. Alotaibi, Kamal Shah, Thabet Abdeljawad

“…In this work, the Gauss–Hermite quadrature method and the contour integration method based on the trapezoidal and midpoint rule are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to different types of fractional differential equations, numerical accuracy, computational efficiency, and ease of programming and implementation. …”
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Study of Fuzzy Fractional Nonlinear Equal Width Equation in the Sense of Novel Operator by Muhammad Naeem, Ahmed A. Khammash, Ibrahim Mahariq, Ghaylen Laouini, Jeevan Kafle

“…In this paper, we designed an algorithm by applying the Laplace transform to calculate some approximate solutions for fuzzy fractional-order nonlinear equal width equations in the sense of Atangana-Baleanu-Caputo derivatives. …”
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Image information optimization processing based on fractional order differentiation and WT algorithm. by Qiong Long

“…To improve the quality of complex images, research proposes an image information optimization processing method based on fractional order differentiation and WT algorithm. …”
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A Fuzzy Fractional Order Approach to SIDARTHE Epidemic Model for COVID-19 by P. Chellamani, K. Julietraja, Ammar Alsinai, Hanan Ahmed

“…Hence, an efficient method to solve a fuzzy fractional differential equation using Laplace transforms and their inverses using the Caputo sense derivative is developed, which can make the problem easier to solve numerically. …”
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A Review on Fiber Properties, Manufacturing, and Crashworthiness of Natural Fiber-Reinforced Composite Structures by Mahaboob Subhani Shaik, Hariharan Sankara Subramanian, Ravi Kumar B., Indran Suyambulingam, P Senthamaraikannan, R. Kumar

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New Perspective on the Conventional Solutions of the Nonlinear Time-Fractional Partial Differential Equations by Hijaz Ahmad, Ali Akgül, Tufail A. Khan, Predrag S. Stanimirović, Yu-Ming Chu

“…In addition, numerical results for different cases of the fractional-order α are presented graphically, which show the effectiveness of the proposed procedure and revealed that the proposed scheme is very effective, suitable for fractional PDEs, and may be viewed as a generalization of the existing methods for solving integer and noninteger order differential equations.…”
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Three-Dimensional and Multiple Image Encryption Algorithm Using a Fractional-Order Chaotic System by Ghader Ghasemi, Reza Parvaz, Yavar Khedmati Yengejeh

“…One of the most important tools used in the proposed algorithm is the hybrid chaotic system, which is obtained by fractional derivatives and the Cat map. Different types of tests used to study the behavior of this system demonstrate the efficiency of the proposed hybrid system. …”
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Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM by Abir Chaouk, Maher Jneid

“…In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. …”
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A Nonsingular Fractional Derivative Approach for Heat and Mass Transfer Flow with Hybrid Nanoparticles by Muhammad Imran Asjad, Rabia Naz, Muhammad Danish Ikram, Azhar Iqbal, Fahd Jarad

“…With the Mittag–Leffler kernel, the conventional governing equations are converted into dimensionless form and then generalised with noninteger order fractional operators. The solutions for temperature and velocity fields obtained via Laplace transform method and expressed in the series form. …”
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Comparison of statistical methods for the analysis of patient-reported outcomes (PROs), particularly the Short-Form 36 (SF-36), in randomised controlled trials (RCTs) using standar... by Yirui Qian, Stephen J. Walters, Richard M. Jacques, Laura Flight

“…Transformed scale-based methods (OL, OP, BB, BLN, Frac, and BR) shared a similar pattern, except that OL generated higher absolute coefficients and BLN produced higher SESs than other methods. …”
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Shape factor analysis of water and aluminium oxide nanoparticles in a porous medium with slip effects by Prasun Choudhary, K. Loganathan, Kavita Jat, Kalpna Sharma, S. Eswaramoorthi

“…Different velocity curves correspond to magnetic parameter M showing that fluid velocity f′(η) decreases, while higher inputs of nanoparticle volume fraction Φ1 enhance fluid velocity. …”
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Dynamical and computational analysis of fractional Whitham-Broer-Kaup equations arising in shallow-water waves by Amit Kumar, Devendra Kumar, Dumitru Baleanu

“…In this work, we extend the modified homotopy analysis transform method (MHATM) for studying the three different coupled time-fractional physical problems. …”
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Many-Body Quantum Catalysts for Transforming Between Phases of Matter by David T. Stephen, Rahul Nandkishore, Jian-Hao Zhang

“…In particular, we construct catalysts that enable transformations between different symmetry-protected topological (SPT) phases of matter using symmetric finite-depth quantum circuits. …”
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Effects of Temperature and Carrier Gas on Phosphorus Transformation in Biosolids Biochar by Shefali Aktar, Md Afzal Hossain, Gabriel Gasco, Ana Mendez, Cicero Celio de Figueiredo, Kalpit Shah, Jorge Paz-Ferreiro

“…The effect of three different pyrolysis temperatures (400 °C, 500 °C, and 600 °C) and two carrier gases (CO₂ and N₂) on P fractionation and the speciation of P on biochars produced from two biosolids were investigated. …”
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Enzymatic Transformation and Bonding of Sulfonamide Antibiotics to Model Humic Substances by J. Schwarz, H. Knicker, G. E. Schaumann, S. Thiele-Bruhn

“…Fractions of different bonding strength were determined using a sequential extraction procedure. …”
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Numerical analysis of fractional nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass by Yi Sun, Junfeng Lu, Menghu Zhu, Abdulrahman Ali Alsolami

“…A numerical approach based upon the fractional complex transformation and the global residue harmonic balance method (FCT-GRHBM) is suggested for approximately solving this fractional oscillation system of fifth-order nonlinearity. …”
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Pure Fractional Optimal Control of Partial Differential Equations: Nonlinear, Delay and Two-Dimensional PDEs by Iman Malmir

“…Novel methods for solving the optimal control problems of different and new types of the fractional partial differential equations (PDEs) as: nonlinear PDEs, delay PDEs, and two-dimensional PDEs, are introduced in this paper. …”
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Super duplex stainless steel fabricated by arc-based directed energy deposition: Microstructure evolution and phase field solidification simulation by Daysianne Kessy Mendes Isidorio, João da Cruz Payão Filho, Murali Uddagiri, Kimiya NouraniNiaki, Oleg Shchyglo, Ingo Steinbach

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