Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems by Asad Freihat, Shaher Momani

“…The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.…”
Get full text

New Expansion Formulas for a Family of the λ-Generalized Hurwitz-Lerch Zeta Functions by H. M. Srivastava, Sébastien Gaboury

“…These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. …”
Get full text

Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes by Abdon Atangana, Dumitru Baleanu

“…A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. …”
Get full text

On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative by Ali El Mfadel, Said Melliani, M’hamed Elomari

“…The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. …”
Get full text

Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach by Zhi-Yong Chen, Carlo Cattani, Wei-Ping Zhong

“…Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.…”
Get full text

Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term by S. Manikandan, V. Muthulakshmi, S. Harikrishnan, Porpattama Hammachukiattikul

“…Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. …”
Get full text

Fractional Order Models of Industrial Pneumatic Controllers by Abolhassan Razminia, Dumitru Baleanu

“…In the light of fractional calculus, a fractional order derivative-derivative (FrDD) controller and integral-derivative (FrID) are remodeled. …”
Get full text

Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String by Ming-Sheng Hu, Ravi P. Agarwal, Xiao-Jun Yang

“…We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. …”
Get full text

The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations by W. K. Zahra, S. M. Elkholy

“…Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. …”
Get full text

Option Pricing under the Subordinated Market Models by Longjin Lv, Changjuan Zheng, Luna Wang

“…Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. …”
Get full text

Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series by Xiang-Chao Shi, Lan-Lan Huang, Zhen-Guo Deng, Dan Liu

“…Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. …”
Get full text

Multipoint BVP for the Langevin Equation under φ-Hilfer Fractional Operator by Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad

“…At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach contraction principle. …”
Get full text

ABC Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination by Jirong Yang, Farkhanda Afzal, Perpetual Appiah

“…At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.…”
Get full text

Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation by J. A. Tenreiro Machado

“…Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.…”
Get full text

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control by Fathalla A. Rihan, Chinnathambi Rajivganthi, Palanisamy Muthukumar

“…We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. …”
Get full text

Local Fractional Poisson and Laplace Equations with Applications to Electrostatics in Fractal Domain by Yang-Yang Li, Yang Zhao, Gong-Nan Xie, Dumitru Baleanu, Xiao-Jun Yang, Kai Zhao

“…From the local fractional calculus viewpoint, Poisson and Laplace equations were presented in this paper. …”
Get full text

Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers by Sunil Kumar Mishra, Dinesh Chandra

“…This work focuses on the use of fractional calculus to design robust fractional-order PID (PIλDμ) controller for stabilization and tracking control of inverted pendulum (IP) system. …”
Get full text

On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions by Xiaobin Wang, Muhammad Shoaib Saleem, Kiran Naseem Aslam, Xingxing Wu, Tong Zhou

“…The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h-convex function. …”
Get full text

Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay by S. J. Sadati, D. Baleanu, A. Ranjbar, R. Ghaderi, T. Abdeljawad (Maraaba)

“…Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. …”
Get full text

Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations by Latif Ur Rahman, Muhammad Arshad, Sabri T. M. Thabet, Imed Kedim

“…Using one of our main results, we solve a FDE from a broad class of fractional calculus. Eventually, we support our main results with a numerical example. …”
Get full text