A Convergent Legendre Spectral Collocation Method for the Variable-Order Fractional-Functional Optimal Control Problems by Zahra Pirouzeh, Mohammad Hadi Noori Skandari, Kameleh Nassiri Pirbazari

“…In this paper, a numerical method is applied to approximate the solution of variable-order fractional-functional optimal control problems. …”
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An Enhanced Phase Gradient Autofocus Algorithm for SAR: A Fractional Fourier Transform Approach by Kanghyuk Seo, Yonghwi Kwon, Chul Ki Kim

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Coupled of Semi Analytic Approach Associated with Laplace Transform First Step for Solving Matrix Differential Equations Quadratic Form when the Time-Delay in Noise Term by Khalid Hammood AL-Jizani

“…This technique can used to different nonlinear problem. The Adomian decomposition method is a semi analytical technique for solving different type of differential equations ordinary, partial, fractional, delay differential equations and many type. …”
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General Solution of Linear Fractional Neutral Differential Difference Equations by Hai Zhang, Jinde Cao, Wei Jiang

“…The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference equations are derived by using the Gronwall integral inequality and the Laplace transform method, respectively. …”
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Comparative Analysis of the Time-Fractional Black–Scholes Option Pricing Equations (BSOPE) by the Laplace Residual Power Series Method (LRPSM) by Muhammad Imran Liaqat, Eric Okyere

“…The residual power series method is effective for obtaining solutions to fractional-order differential equations. …”
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On the analytical soliton-like solutions to (2+1)-dimensional fractional asymmetric Nizhnik-Novikov-Veselov system arising in incompressible fluids by Humaira Yasmin, Humaira Yasmin, Albandari W. Alrowaily, Mounirah Areshi, Rasool Shah, S. A. El-Tantawy, S. A. El-Tantawy

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Innovative techniques to chaotic dynamics and kinetic differ-integral equations by Ahsan Mehmood, Zhi-Guo Liu, Muhammad Samraiz, Fuat Usta, Sama Arjika

“…Utilizing advanced numerical methods, we transform the non-local kernel into its local counterpart in order to obtain efficient and accurate solutions.…”
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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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Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays by N. H. Sweilam, M. M. Khader, A. M. S. Mahdy

“…A numerical method for solving the fractional-order logistic differential equation with two different delays (FOLE) is considered. …”
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Ensemble models enhanced estimates of leaf chlorophyll from fractional order derivatives transformed spectra by Guangman Song, Yi Gan, Lingfeng Mao, Zhiwei Ge, Jiangshan Lai, Quan Wang

“…To address these challenges, we applied the fractional order derivatives (FOD) transformed spectra into ensemble models, consisting of two popular data-oriented approaches, to refine the spectral response characteristics of leaf chlorophyll using a composite dataset (two public datasets: LOPEX and ANGERS; two collected datasets: Naeba and Nakakawane) containing different species samples. …”
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Analytic solutions of the time-fractional Boiti-Leon-Manna-Pempinelli equation via novel transformation technique by Bushra Yasmeen, Khalil Ahmad, Ali Akgül, Qasem Al-Mdallal

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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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The Analysis of Fractional-Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform by A. A. Alderremy, Shaban Aly, Rabia Fayyaz, Adnan Khan, Rasool Shah, Noorolhuda Wyal

“…In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. The suggested techniques in addition with Laplace transform and Atangana–Baleanu fractional derivative operator are implemented to solve four systems. …”
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Deep learning of the particulate and mineral-associated organic carbon fractions using a compositional transform and mid-infrared spectroscopy by Mingxi Zhang, Zefang Shen, Lewis Walden, Farid Sepanta, Zhongkui Luo, Lei Gao, Oscar Serrano, Raphael A. Viscarra Rossel

“…Mid-infrared (MIR) spectroscopy combined with multivariate modelling can alleviate these limitations because the method can estimate SOC and its fractions rapidly, cost-effectively and accurately. …”
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State-Space Approach to the Time-Fractional Maxwell’s Equations under Caputo Fractional Derivative of an Electromagnetic Half-Space under Four Different Thermoelastic Theorems by Eman A. N. Al-Lehaibi, Hamdy M. Youssef

“…Laplace transform’s inversions were calculated using Tzou’s iteration method. …”
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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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Novel approximations to the fourth-order fractional Cahn–Hillard equations: Application to the Tantawy Technique and other two techniques with Yang transform by Samir A El-Tantawy, Amnah S Al-Johani, Aljawhara H Almuqrin, Adnan Khan, Lamiaa S El-Sherif

“…This investigation employs the “Tantawy Technique,” a novel, highly accurate, and fast technique, to solve and analyze the fourth-order time-fractional Cahn–Hilliard (TFCH) models. We also implement the variational iteration transform method (VITM) and the homotopy perturbation transform method (HPTM) within the Yang transform framework to analyze the fourth-order TFCH models. …”
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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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Adaptive Fast Refocusing for Ship Targets With Complex Motion in SAR Images by Xinqi Xu, Xiangguang Leng, Zhongzhen Sun, Xiangdong Tan, Kefeng Ji, Gangyao Kuang

“…Third, the ORO within the ORI is computed using the fractional autocorrelation. Then, each azimuth line is refocused using fractional Fourier transform. …”
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A novel color image encryption algorithm based on fractional-order conservative memristive hyperchaotic system and extended zig-zag transform by Fanqi Meng, Gang Wu, Juxiao Zhang

“…Second, a new extended Zig-Zag confusing method is designed, which realizes the scrambling of pixels in different channels of a color image. …”
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