Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers by Md. Al Amin, M. Ali Akbar, M. Ashrafuzzaman Khan, Md. Sagib

“…We apply a traveling wave transformation with the Beta derivative to convert the nonlinear fractional differential equation into a standard nonlinear differential equation. …”
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Numerical solutions of a fractional order SEIR epidemic model of measles under Caputo fractional derivative. by Nawa A Alshammari, N S Alharthi, Abdulkafi Mohammed Saeed, Adnan Khan, Abdul Hamid Ganie

“…The Homotopy perturbation transform method (HPTM) and Yang transform decomposition methodology (YTDM) have been employed to obtain the numerical solution of the time fractional model. …”
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Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers by Hashem S. Alkhaldi, Ibrahim M. Abu-Alshaikh, Anas N. Al-Rabadi

“…The damping characteristics of the beam and SDOF systems are described in terms of fractional derivatives. Three coupled second-order fractional differential equations are produced and then they are solved by combining the Laplace transform with the decomposition method. …”
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Numerous Multi-Wave Solutions of the Time-Fractional Boussinesq-like System via a Variant of the Extended Simple Equations Method (SEsM) by Elena V. Nikolova, Mila Chilikova-Lubomirova

“…The key developments over the original SEsM in the proposed analytical framework include the following: (1) an extension of the original SEsM by constructing the solutions of the studied FNPDEs as complex composite functions which combine two single composite functions, comprising the power series of the solutions of two simple equations or two special functions with different independent variables (different wave coordinates); (2) an extension of the scope of fractional wave transformations used to reduce the studied FNPDEs to different types of ODEs, depending on the physical nature of the studied FNPDEs and the type of selected simple equations. …”
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On the Extended Simple Equations Method (SEsM) for Obtaining Numerous Exact Solutions to Fractional Partial Differential Equations: A Generalized Algorithm and Several Applications by Elena V. Nikolova

“…The expansions made to the original SEsM algorithm are implemented in several directions: (1) In constructing analytical solutions: exact solutions to FNPDE systems are presented by simple or complex composite functions, including combinations of solutions to two or more different simple equations with distinct independent variables (corresponding to different wave velocities); (2) in selecting appropriate fractional derivatives and appropriate wave transformations: the choice of the type of fractional derivatives for each system of FNPDEs depends on the physical nature of the modeled real process. …”
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How aromatic dissolved organic matter differs in competitiveness against organic micropollutant adsorption by Qi Wang, Oliver J. Lechtenfeld, Luuk C. Rietveld, Jonas Schuster, Mathias Ernst, Roberta Hofman-Caris, Jan Kaesler, Chunmiao Wang, Min Yang, Jianwei Yu, Frederik Zietzschmann

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On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system by Usman Younas, Jan Muhammad, Qasim Ali, Mirwais Sediqmal, Krzysztof Kedzia, Ahmed Z. Jan

“…The third-order non-linear $$\beta$$ β -fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. …”
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Breaking barriers: harnessing hypofractionated radiotherapy to transform outcomes in low tumor mutation burden stage III non-small cell lung cancer - a retrospective study by Jingyun Yang, Tianxiang Cui, Yang Zhang, Guangpeng Chen, Xinxin Wang, Jianguo Sun, Anmei Zhang, Guanghui Li

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Thermomechanical Fractional Model of Two Immiscible TEMHD by F. Hamza, A. M. Abd El-Latief, W. Khatan

“…The inversion of Laplace transform is obtained by using numerical method based on a Fourier-series expansion. …”
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A Simple and Effective Second-Order Numerical Algorithm for Tempered Fractional Differential Equation With Time Caputo-Tempered Fractional Derivative by Dechao Gao, Zeshan Qiu, Lizan Wang, Jianxin Li

“…The time Caputo-tempered fractional derivative is transformed into time Riemann–Liouville tempered fractional derivative by the relationship between Caputo fractional derivative and Riemann–Liouville fractional derivative. …”
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A Study on the Fractal-Fractional Epidemic Probability-Based Model of SARS-CoV-2 Virus along with the Taylor Operational Matrix Method for Its Caputo Version by Shahram Rezapour, Sina Etemad, İbrahim Avcı, Hijaz Ahmad, Azhar Hussain

“…Finally, we transform our fractal-fractional model into a Caputo probability-based model of SARS-CoV-2 to derive solutions via the operational matrix method under Taylor’s basis. …”
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Comparison in the Structure and Physicochemical Properties of Soybean Dregs Insoluble Dietary Fiber from Different Sources by Chenhao ZHAO, Wenhao LIU, Bo LI, Sainan WANG, Hansong YU, Wei YU

“…TBP-IDF was prepared by a complex enzymatic method and its basic components and fractions were determined. …”
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Computational Solution of a Fractional Integro-Differential Equation by Muhammet Kurulay, Mehmet Ali Akinlar, Ranis Ibragimov

“…Although differential transform method (DTM) is a highly efficient technique in the approximate analytical solutions of fractional differential equations, applicability of this method to the system of fractional integro-differential equations in higher dimensions has not been studied in detail in the literature. …”
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Study on occurrence law of sulfur in high-sulfur coal with different particle sizes and densities by Yulong YANG, Fei GAO, Yunming ZHANG

“…To investigate the state of sulfur in different particle sizes and density fractions of high-sulfur coal, the Ciyaogou high-sulfur coal was divided into particle size and density fractions according to the screening method and flotation method. …”
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Performance of segmentation (watershed and meanshift) and image transformation (MNF-laplacian filter) methods for extracting complex coastlines from Pleiades images: the case of th... by Luc Simirore Diatta, Katia Schörle, Zahra Akacha, Semah Bettaieb, Ali Drine, Ameur Oueslati, Luc Lapierre

“…This study evaluates the performance of different coastline extraction methods based on the segmentation (Watershed and Meanshift) and transformation and discrimination (MNF-Laplacian filter) of very high spatial resolution Pléiades images resampled to 0.5 m. …”
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Magnetic Field Effects on Convective Heat Transfer of Ferrofluid from a Heated Sphere in Porous Media by Ayesha Aktar, Sharaban Thohura, Md. Mamun Molla

“…The resulting nonlinear systems of equations are then numerically solved inside the computing domain into a regular rectangle using the effective Finite Difference Method (FDM).  Numerical outcomes are then represented in terms of local Nusselt number, velocity, temperature profile, and skin friction coefficient, respectively for a range of porosity parameters, ϵ = 0.4, 0.6, 0.8, magnetic effect parameter or Hartmann number, Ha = 0.0, 1.0, 3.0, 5.0 and the ferroparticle volume fraction coefficients, ϕ = 0%, 2%, 4%, 6%. …”
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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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Finite difference simulation of natural convection of two-phase hybrid nanofluid along a vertical heated wavy surface by Shapla Akter, Amzad Hossain, Md. Mahadul Islam, Md. Mamun Molla

“…The mathematical model accounts for laminar and incompressible fluid flow with a Prandtl number of Pr = 6.2, Lewis number Le = 10, and maximum [Formula: see text] concentration of hybrid nanoparticles. After transforming the governing equations into a non-dimensional form, the implicit finite difference method is used to solve them. …”
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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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