..., we discuss some basic properties of the proposed operators that are expected to be widely used in fractional calculus. e-mails:  odibat@bau.edu.jo ; z.odibat@gmail.com 30 12 2023 11 09 2024 18 10 2024 where μ α = α / ( 1 − α ) , and M...

... formulations encompass discrete-time sliding mode approaches [ 10 , 11 ]. In addition, fuzzy sliding mode controllers have been explored [ 12 , 13 ], furnishing improved performances in several scenarios. discrete-time systems fractional calculus fuzzy logic control sliding mode control 19...

... to the Fractional Calculus and Fractional Differential Equations , Wiley , New York . [61] Podlubny , I. , 1999 , Fractional Differential Equations , Academic Press , New York . [62] Li , C. P. , and Deng , W. H. , 2007 , “ Remarks on Fractional Derivatives ,” Appl. Math...

.... Differential equations in fractal media (open field!) Approximation: fractal media is a continuous medium in a space with a noninteger dimension (Fractional Calculus). The study of propagation of electromagnetic waves in a medium with a self-similar structure, like a fractal, is especially relevant...

... principle fractional calculus During the last 60 years, dynamic optimization and issues related to optimal control theory have received a lot of attention. Various theories, and a large number of applications of optimal control, can be considered as an indicator of the impact of the theory...

... National Foundation for Science and Technology Development (NAFOSTED). References [1] Miller , K. S. , and Ross , B. , 1993 , An Introduction to the Fractional Calculus and Fractional Differential Equations , Wiley , New York . [2] Oldham , K. B. , and Spanier , J. , 1974...

... in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received September 13, 2015; final manuscript received May 6, 2016; published online May 24, 2016. Assoc. Editor: Brian Feeny. 13 09 2015 06 05 2016 Control Fractional calculus Nonlinear dynamical systems...

...-order elements fractional calculus fractional differential equations This paper considers the energy aspects of fractional-order elements defined by the equation: force is proportional to the fractional-order derivative of displacement, with order varying from zero to two. In contrast...

... Modes in Control Optimization , Springer Verlag , Berlin . [36] Lubich , C. , 1986 , “ Discretized Fractional Calculus ,” SIAM J. Math. Anal. , 17 , pp. 704 – 719 . 10.1137/0517050 [37] Lu , J. G. , 2005 , “ Chaotic Dynamics and Synchronization of Fractional-Order Arneodo's...

... equations we conclude that our method gave comparable results. fractional calculus 0perational matrix Legendre polynomials Caputo derivative tau method Fractional calculus is an emerging field both in the theoretical and applied aspects [ 1–18 ]. During the last decades, several methods...

... > 1 (not shown) grow with increasing amplitude in time and with increasing rapidity as q increases. 19 10 2009 05 03 2010 21 10 2010 21 10 2010 differential equations zoology fractional calculus fractional differential equations fractional growth rate...