W transform and its application in fractional linear systems with rational powers

[1]  N. Ford,et al.  Numerical Solution of the Bagley-Torvik Equation , 2002, BIT Numerical Mathematics.

[2]  Ahmed Alsaedi,et al.  Fractional electrical circuits , 2015 .

[3]  Guy Jumarie,et al.  On the fractional solution of the equation f(x + y) = f(x)f(y) and its application to fractional Laplace's transform , 2012, Appl. Math. Comput..

[4]  Mahdi Afshar,et al.  Extending the Root-Locus Method to Fractional-Order Systems , 2008, J. Appl. Math..

[5]  N. Hitchin THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE , 1987 .

[6]  Ahmed Gomaa Radwan,et al.  Fundamentals of fractional-order LTI circuits and systems: number of poles, stability, time and frequency responses , 2016, Int. J. Circuit Theory Appl..

[7]  K. K. Sharma,et al.  Fractional Laplace transform , 2010, Signal Image Video Process..

[8]  Guishu Liang,et al.  Positive‐real property of passive fractional circuits in W‐domain , 2018, Int. J. Circuit Theory Appl..

[9]  Zaid M. Odibat,et al.  Analytic study on linear systems of fractional differential equations , 2010, Comput. Math. Appl..

[10]  A. G. Radwan,et al.  Resonance and Quality Factor of the $RL_{\alpha} C_{\alpha}$ Fractional Circuit , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[11]  G. K. Watugala,et al.  Sumudu Transform - a New Integral Transform to Solve Differential Equations and Control Engineering Problems , 1992 .

[12]  Thabet Abdeljawad,et al.  On conformable fractional calculus , 2015, J. Comput. Appl. Math..

[13]  Sophie Hallstedt,et al.  A model-based approach for sustainability and value assessment in the aerospace value chain , 2015 .

[14]  Soo-Chang Pei,et al.  Eigenfunctions of Fourier and Fractional Fourier Transforms With Complex Offsets and Parameters , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  A. Gudadhe,et al.  Fractional Quaternion Laplace Transform and Convolution , 2012 .

[16]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[17]  J. F. Gómez‐Aguilar,et al.  Analytical solutions of electrical circuits considering certain generalized fractional derivatives , 2019, The European Physical Journal Plus.

[18]  J. J. Rosales,et al.  Analysis on the time and frequency domain for the RC electric circuit of fractional order , 2013 .

[19]  Todd J. Freeborn,et al.  A Survey of Fractional-Order Circuit Models for Biology and Biomedicine , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[20]  A. Elwakil,et al.  On the stability of linear systems with fractional-order elements , 2009 .

[21]  Khaled N. Salama,et al.  Passive and Active Elements Using Fractional ${\rm L}_{\beta} {\rm C}_{\alpha}$ Circuit , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  P. Eloe,et al.  A transform method in discrete fractional calculus , 2007 .

[23]  Tofigh Allahviranloo,et al.  SOLVING FUZZY FRACTIONAL DIFFERENTIAL EQUATIONS BY FUZZY LAPLACE TRANSFORMS , 2012 .

[24]  Abdon Atangana,et al.  Electrical circuits RC, LC, and RL described by Atangana–Baleanu fractional derivatives , 2017, Int. J. Circuit Theory Appl..

[25]  Agnieszka Jakubowska-Ciszek,et al.  Analysis of the transient state in a parallel circuit of the class RLβCα , 2018, Appl. Math. Comput..

[26]  Amalia Torre Linear and radial canonical transforms of fractional order , 2003 .

[27]  Ahmed S. Elwakil,et al.  An expression for the voltage response of a current‐excited fractance device based on fractional‐order trigonometric identities , 2012, Int. J. Circuit Theory Appl..