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

“…Therefore, the study is based on wavelet transform algorithm and fractional order differentiation to perform edge detection and image fusion. …”
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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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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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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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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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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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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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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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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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Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators by Kamsing Nonlaopon, Muhammad Naeem, Ahmed M. Zidan, Rasool Shah, Ahmed Alsanad, Abdu Gumaei

“…This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. …”
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A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law by Noufe H. Aljahdaly, Ali Akgül, Rasool Shah, Ibrahim Mahariq, Jeevan Kafle

“…This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. …”
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Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative by Muhammad Naeem, Hadi Rezazadeh, Ahmed A. Khammash, Rasool Shah, Shamsullah Zaland

“…We apply the iterative method and the Laplace transform under the fractional Caputo-Fabrizio operator. …”
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An innovative q-homotopy analysis approach for solving generalized q-fractional non-linear biological population model by Khalid K. Ali, Ahmed S. Shehata, Mohamed S. Mohamed, Turki J. Alqurashi, M. Maneea

“…The qHAM is extended to merge q-fractional Laplace transform to obtain approximations in both non-linear and linear terms of q-fractional partial differential equations (q-FPDEs). …”
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Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport by Anis Allagui, Georgii Paradezhenko, Anastasiia Pervishko, Dmitry Yudin, Hachemi Benaoum

“…Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox’s H-function that we evaluate for different values of $$\alpha$$ α and $$\beta$$ β .…”
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Exploring the Dynamics of Fractional q-Integro-Differential Equations with Infinite Time Delays: A Study in Mathematical Analysis by Shami A. M. Alsallami, K. R. Raslan, E. M. Khalil, S. Abdel-Khalek, Amira Abd-Elall Ibrahim, Khalid K. Ali

“…By combining the finite difference approach with the trapezoidal method, the equation is transformed into a system of algebraic equations that can be efficiently solved. …”
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Application of Biochar on Soil Improvement and Speciation Transformation of Heavy Metal in Constructed Wetland by Yuan Zhou, Xiaoqin Nie, Yao Zhao, Liqiu Zhang, Yatian Cheng, Cancan Jiang, Wenbin Zhao, Xiangchun Wang, Chao Yang

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