### Citations

667 |
The Fractional Calculus.
- Oldham, Spanier
- 1974
(Show Context)
Citation Context ...e fractional parameter. Fractional parameter describes the order of fractional curl operator. 1. INTRODUCTION Ten years before, interest in exploring the roles and applications of fractional calculus =-=[1]-=- and fractional operators in electromagnetics led to fractionalization of curl operator, an operator which is commonly used in electromagnetics. It is represented by curl α = (∇×) α and is known as fr... |

274 |
Foundations for Microwave Engineering
- Collin
- 1992
(Show Context)
Citation Context ...respectively. Consider the TMmnp mode in the rectangular cavity resonator. Where the three symbol {mnp} subscript designate a TM or TE standing wave pattern in cavity resonator. Field expressions are =-=[24]-=- ˆzEz(x, y, z) =ˆzAmnp sin(kxx) sin(kyy) cos(kzz) ˆxEx(x, y, z) =−ˆx kzkx k2 Amnp cos(kxx) sin(kyy) sin(kzz) c ˆyEy(x, y, z) =−ˆy kzky k2 Amnp sin(kxx) cos(kyy) sin(kzz) c (1a) (1b) (1c)Progress In E... |

12 | Complex and higher order fractional curl operator in electromagnetics,” - Naqvi, Abbas - 2004 |

12 |
Fractional duality and perfect electromagnetic conductor
- Hussain, Naqvi, et al.
(Show Context)
Citation Context ...zz) =−Ey c ηHzfd = Amnp sin (kxx) sin (kyy) cos (kzz) =−Ez (11a) (11b) (11c) (11d) (11e) (11f) For 0 <α<1, the fields given by (9) describe the fractional dual solution between two solutions given by =-=(10)-=- and (11). Which ‘in other sense’ replicates the intermediate fractional behavior between PEC and PMC cavities. 3. NUMERICAL ANALYSIS OF FRACTIONAL FIELDS To study the behavior of fractional TMmnpfd f... |

12 | Fractional curl operator and fractional chiro-waveguide - Hussain, Faryad, et al. |

11 | Fractional curl operator in chiral medium and fractional nonsymmetric transmission line - Hussain, Naqvi - 2006 |

10 | Q.A.: Fractional rectangular waveguide. - Faryad, Naqvi - 2007 |

9 | Fractional dual solutions and corresponding sources - Naqvi, Rizvi - 2000 |

9 |
Fractional curl operator and fractional waveguides
- Hussain, Ishfaq, et al.
- 2006
(Show Context)
Citation Context ...in (kyy) sin (kzz) =−Ex c ηHyfd = kzky k2 Amnp sin (kxx) cos (kyy) sin (kzz) =−Ey c ηHzfd = Amnp sin (kxx) sin (kyy) cos (kzz) =−Ez (11a) (11b) (11c) (11d) (11e) (11f) For 0 <α<1, the fields given by =-=(9)-=- describe the fractional dual solution between two solutions given by (10) and (11). Which ‘in other sense’ replicates the intermediate fractional behavior between PEC and PMC cavities. 3. NUMERICAL A... |

8 | Fractional curl operator in reflection problems - Veliev, Engheta - 2004 |

8 | A representation theorem involving fractional derivatives for linear homogeneous chiral media,Microwave Opt Tech Lett 28 - Lakhtakia - 2001 |

7 |
Fractional curl operator in electromagnetics,” Microwave Opt
- Engheta
- 1998
(Show Context)
Citation Context ...rs in electromagnetics led to fractionalization of curl operator, an operator which is commonly used in electromagnetics. It is represented by curl α = (∇×) α and is known as fractional curl operator =-=[2]-=-. Generally, the parameter α is noninteger. For α = 0, the fractional curl operator becomes an identity operator. Whereas, the fractional curl operator transforms to conventional curl operator when α ... |

7 | Fractional duality and metamaterials with negative permittivity and permeability - Naqvi, Abbas |

7 | Modelling of transmission through a chiral slab using fractional curl operator, Optics Communications - Naqvi, Naqvi, et al. - 2006 |

6 | Fractional dual solutions to Maxwell equations in homogeneous chiral medium - Naqvi, Murtaza, et al. |

6 | Fractional surface waveguide - Maab, Naqvi - 2008 |

3 | Fractional operators approach in electromagnetic wave reflection problems - Veliev, Ivakhnychenko, et al. |

2 | Fractional curl operator in radiation problems - Ivakhnychenko, Veliev - 2004 |

2 | Elementary fractional dipoles - Veliev, Ivakhnychenko - 2006 |

2 | Ahmedov, “New generalized electromagnetic boundaries fractional operators approach - Ivakhnychenko, Veliev, et al. - 2006 |

1 |
Perfect electromagnetic conductor and Naqvi (PEMC) and fractional waveguide
- Hussain, Naqvi
- 2007
(Show Context)
Citation Context ...c ηHzfd = Amnp sin (kxx) sin (kyy) cos (kzz) =−Ez (11a) (11b) (11c) (11d) (11e) (11f) For 0 <α<1, the fields given by (9) describe the fractional dual solution between two solutions given by (10) and =-=(11)-=-. Which ‘in other sense’ replicates the intermediate fractional behavior between PEC and PMC cavities. 3. NUMERICAL ANALYSIS OF FRACTIONAL FIELDS To study the behavior of fractional TMmnpfd fields in ... |

1 | Method of fractional operators in the problem of excitation of electric current thread above the plane boundary - Ivakhnychenko - 2008 |

1 | Polarization properties of fractional fields - Ivakhnychenko |