A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems by A. H. Bhrawy, M. A. Alghamdi

“…We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. …”
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Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach by KumSong Jong, HuiChol Choi, KyongJun Jang, SunAe Pak

“…In this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. …”
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Common Fixed-Point Results in Ordered Left (Right) Quasi-b-Metric Spaces and Applications by Hemant Kumar Nashine, Sourav Shil, Hiranmoy Garai, Lakshmi Kanta Dey, Vahid Parvaneh

“…Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.…”
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An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform by Devendra Kumar, Jagdev Singh, A. Kılıçman

“…The results obtained by the two methods are in agreement, and, hence, this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of sumudu transform, homotopy perturbation method, and He’s polynomials. …”
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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation by Naveed Iqbal, Azmat Ullah Khan Niazi, Ramsha Shafqat, Shamsullah Zaland

“…Finally, a few instances of fuzzy fractional differential equations are shown.…”
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Analysis of the Financial Chaotic Model with the Fractional Derivative Operator by Mamadou Diouf, Ndolane Sene

“…Numerical discretization for the fractional differential equations is applied to the chaotic financial model described by the Caputo derivative. …”
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Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation by Jan Freundlich

“…This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. …”
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A Fractional Epidemiological Model for Bone Remodeling Process by Muath Awadalla, Yves Yannick Yameni Noupoue, Kinda Abuasbeh

“…We finally obtained that modeling bone formation process using fractional differential equations yielded comparable results with those obtained through a system of classical differential equations. …”
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A new solitary wave solution of the fractional phenomena Bogoyavlenskii equation via Bäcklund transformation by Yousef Jawarneh, Humaira Yasmin, Ali M. Mahnashi

“…This work also contributes to the knowledge of the physical structures of the fractional Bogoyavlenskyi equation apart from showcasing the potential of the Riccati–Bernoulli sub-ODE method when applied to nonlinear fractional differential equations.…”
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Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems by D. Baleanu, A. H. Bhrawy, T. M. Taha

“…We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. …”
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Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative by Fareeha Sami Khan, M. Khalid, Omar Bazighifan, A. El-Mesady

“…The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α∈0,1 and different step sizes h. …”
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Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques by Imran Siddique, Khush Bukht Mehdi, M. Ali Akbar, Hamiden Abd El-Wahed Khalifa, Asim Zafar

“…These methods can also be used to extract the novel exact traveling wave solutions for solving any types of integer and fractional differential equations arising in mathematical physics.…”
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The g-generalized Mittag-Leffler (p,s,k)-function by Umbreen Ayub, Madiha Shafiq, Amir Abbas, Umair Khan, Anuar Ishak, Y.S. Hamed, Homan Emadifar

“…It may be used to solve a variety of fractional differential equations (FDEs) including fractional Laplace and fractional Poisson equations. …”
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Numerical Investigation of Fractional-Order Differential Equations via φ-Haar-Wavelet Method by F. M. Alharbi, A. M. Zidan, Muhammad Naeem, Rasool Shah, Kamsing Nonlaopon

“…In this paper, we propose a novel and efficient numerical technique for solving linear and nonlinear fractional differential equations (FDEs) with the φ-Caputo fractional derivative. …”
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On the Existence and Stability of Positive Solutions of Eigenvalue Problems for a Class of P-Laplacian ψ-Caputo Fractional Integro-Differential Equations by Yahia Awad

“…This article introduces a generalized approach for analyzing stability and establishing the existence of positive solutions in a specific type of differential equations known as p-Laplacian ψ-Caputo fractional differential equations with fractional integral boundary conditions. …”
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Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem by Abdelkrim Salim, Sabri T.M. Thabet, Ava Sh. Rafeeq, Mohammad Esmael Samei, Imed Kedim, Miguel Vivas-Cortez

“…Our study leverages the properties of tempered (κ,ϖ)-Hilfer fractional operators to explore the mathematical underpinnings of the problem, which is characterized by implicit nonlinear fractional differential equations. To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. …”
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Resolvent Positive Operators and Positive Fractional Resolvent Families by Nan-Ding Li, Ru Liu, Miao Li

“…Some examples of positive solutions to fractional differential equations are presented to illustrate our results.…”
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Fractional Dynamics: Applications of the Caputo Operator in Solving the Sawada–Kotera and Rosenau–Hyman Equations by Khudhayr A. Rashedi, Musawa Yahya Almusawa, Hassan Almusawa, Tariq S. Alshammari, Adel Almarashi

“…The findings underscore the potential of q-HMTM and MVIM as robust tools for solving non-linear fractional differential equations. They offer insights into their practical implications in fluid dynamics, wave mechanics, and other applications governed by fractional-order models.…”
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Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System by Z.H. Wang, M. L. Du

“…The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. …”
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Further Developments of Bessel Functions via Conformable Calculus with Applications by Mahmoud Abul-Ez, Mohra Zayed, Ali Youssef

“…The obtained solutions of some fractional differential equations improve the analog ones provided by various authors using different techniques. …”
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