An accurate numerical technique for solving a special case of fractional differential equations using the Khalouta transform of two different fractional derivatives by A. Khalouta

“…The aim of this paper is to present a novel coupling approach of the Khalouta transform method and the homotopy perturbation method in order to obtain an accurate and efficient method for solving a special case of fractional differential equations involving Caputo and Caputo-Fabrizio fractional derivatives. …”
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Synchroextracting Transform Based on the Novel Short-Time Fractional Fourier Transform by Bei Li, Zhuosheng Zhang

“…In order to improve the concentration of the time–frequency representation (TFR) generated by the NSTFRFT, two post-processing time–frequency analysis methods, two synchroextracting transforms based on the NSTFRFT with two different fractional Fourier transform (FRFT) angles, are proposed in this paper. …”
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Solve Schrodinger Fractional Order Boundary Value Problem by Laplace Transformation Method by Shwan Fatah, Hozan Hilmi, Karwan Jwamer

“…We proved the solution using the Laplace transformation after obtaining the existence using the fractional integral and integral operator methods.…”
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Comparative Study of the Nonlinear Fractional Generalized Burger-Fisher Equations Using the Homotopy Perturbation Transform Method and New Iterative Transform Method by Mashael M. AlBaidani

“…The comparison table shows how well the methods work for different fractional orders, with results getting closer to precision as the fractional-order numbers get closer to integer values. …”
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Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method by Khalid K. Ali, M. Maneea, Mohamed S. Mohamed

“…This study describes the q-homotopy analysis transform method (q-HATM) as a powerful technique for solving nonlinear problems, which has been successfully used with a set of mathematical models in physics, engineering, and biology. …”
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A Novel Noise-Insensitive Chromatic Dispersion Estimation Method Based on Fractional Fourier Transform of LFM Signals by Wanli Wang, Yaojun Qiao, Aiying Yang, Peng Guo

“…We propose a novel chromatic dispersion (CD) estimation method by fractional Fourier transformation of linear-frequency modulation (LFM) signals. …”
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A study of nonlinear fractional-order biochemical reaction model and numerical simulations by Bheeman Radhakrishnan, Paramasivam Chandru, Juan J. Nieto

“…The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. …”
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Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method by Ali Khalid K., Mohamed Mohamed S., Alharbi Weam G., Maneea Marwa

“…We solve this equation utilizing the modified double Laplace transform method, which is considered a semi-analytical technique that combines the double Laplace transform with Adomian polynomials to enable us to extract nonlinear terms. …”
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Detection method for underwater acoustic communication signals based on adaptive morphological filtering and Hough transform by WANG Yang, SHEN Tongsheng, WANG Tao, QIAO Gang, ZHOU Feng

“…The short-time fractional Fourier transform (STFRFT) method was used to adjust the rotational angle in the fractional domain to match the signal phase, significantly improving the time-frequency energy concentration and forming a clearly defined band like SC. …”
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MHD Maxwell nanofluid flow over a porous conical surface: A fractional approach by D.S. Swetha, K.R. Madhura, Babitha, Irfan Anjum Badruddin, Sarfaraz Kamangar, Abdul Azeem Khan

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Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method by Shaher Momani, Asad Freihat, Mohammed AL-Smadi

“…The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. …”
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Research on the Integration of Sensing and Communication Based on Fractional-Order Fourier Transform by Mingyan Qi, Yuelong Su, Zhaoyi Wang, Kun Lu

“…This study investigated the integration of detection and communication techniques. First, the fractional-order Fourier transform (FRFT) is introduced, and the golden section method, parabolic interpolation, and Brent method are applied to search for the optimal fractional-order domain to accurately estimate the parameters of the linear frequency modulation (LFM) signal. …”
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Recent developments on the Stieltjes transform of generalized functions by Ram Sankar Pathak, Lokenath Debnath

“…The Stieltjes transforms of different orders and the fractional order integration and further generalizations of the Stieltjes transform are discussed in sections 11 and 12. …”
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Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis by Usman Younas, Jan Muhammad, Muhammad Amin S. Murad, D.K. Almutairi, Aziz Khan, Thabet Abdeljawad

“…A variety of solitary wave solutions are extracted in different forms. Moreover, the fractional parametric effect has been observed graphically in various plots depicting wave dynamics. …”
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The Effects of Different Straw-Returning Methods on Soil Organic Carbon Transformation in Rice–Rape Rotation Systems by Lening Hu, Yujiao Ge, Liming Zhou, Zhongyi Li, Anyu Li, Hua Deng, Tieguang He

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A Robust Control Method for Q-S Synchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems by Adel Ouannas, Raghib Abu-Saris

“…A robust control approach is presented to study the problem of Q-S synchronization between Integer-order and fractional-order chaotic systems with different dimensions. …”
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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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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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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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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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