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Volumn 15, Issue 1, 2014, Pages 27-34

Solutions of the telegraph equations using a fractional calculus approach

Author keywords

Fractional differential equations; Mittag Leffler function; Transmission line

Indexed keywords


EID: 84896951515     PISSN: 14549069     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (65)

References (39)
  • 6
    • 84890890505 scopus 로고    scopus 로고
    • RLC electrical circuit of non-integer order
    • DOI: 10.2478/s11534-013-0265-6, 2013
    • F. GÓMEZ, J. ROSALES, M. GUÍA, RLC electrical circuit of non-integer order, Cent. Eur. J. Phys, DOI: 10.2478/s11534-013-0265-6, 2013.
    • Cent. Eur. J. Phys
    • Gómez, F.1    Rosales, J.2    Guía, M.3
  • 7
    • 84890866146 scopus 로고    scopus 로고
    • Analysis on the time and frequency domain for the RC electric circuit of fractional order
    • DOI: 10.2478/s11534-013-0236-y
    • M. GUIA, F. GÓMEZ, J. ROSALES. Analysis on the time and frequency domain for the RC electric circuit of fractional order, Cent. Eur. J. Phys., DOI: 10.2478/s11534-013-0236-y, 2013.
    • (2013) Cent. Eur. J. Phys.
    • Guia, M.1    Gómez, F.2    Rosales, J.3
  • 8
    • 0002641421 scopus 로고    scopus 로고
    • The ramdom walk's guide to anomalous difussion: A fractional dynamics approach
    • R. METZLER, J. KLAFTER, The ramdom walk's guide to anomalous difussion: a fractional dynamics approach, Phys. Rep., 339, pp. 1-77, 2000.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 9
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of random walk: Recent development in description of anomalous transport by fractional dynamics
    • R. METZLER, J. KLAFTER, The restaurant at the end of random walk: recent development in description of anomalous transport by fractional dynamics, J. Phys., A37, pp. R161-R208, 2004.
    • (2004) J. Phys. , vol.A37
    • Metzler, R.1    Klafter, J.2
  • 14
    • 0000930143 scopus 로고
    • A new dissipation model based on memory mechanism
    • M. CAPUTO, F. MAINARDI, A new dissipation model based on memory mechanism, Pure and App. Geo., 91, pp. 134-147, 1971.
    • (1971) Pure and App. Geo. , vol.91 , pp. 134-147
    • Caputo, M.1    Mainardi, F.2
  • 15
    • 9644282238 scopus 로고
    • University of Kalmar, Rep. No. 940426
    • S. WESTERLUND, Causality, University of Kalmar, Rep. No. 940426, 1994.
    • (1994) Causality
    • Westerlund, S.1
  • 17
    • 85084386480 scopus 로고    scopus 로고
    • Modeling and simulation of equivalent circuits in description of biological systems - A fractional calculus approach
    • F. GÓMEZ, J. BERNAL, J. ROSALES, T. CÓRDOVA, Modeling and simulation of equivalent circuits in description of biological systems - a fractional calculus approach, J. Electric. Bioimped., 3, pp. 2-11, 2012.
    • (2012) J. Electric. Bioimped. , vol.3 , pp. 2-11
    • Gómez, F.1    Bernal, J.2    Rosales, J.3    Córdova, T.4
  • 18
    • 84868197956 scopus 로고    scopus 로고
    • Existence of a periodic mild solution for a nonlinear fractional differential equation
    • A. E. M. HERZALLAH, D. BALEANU, Existence of a periodic mild solution for a nonlinear fractional differential equation, Comput. Math. Appl., 64, pp. 3059-3064, 2012.
    • (2012) Comput. Math. Appl. , vol.64 , pp. 3059-3064
    • Herzallah, A.E.M.1    Baleanu, D.2
  • 20
    • 84878471334 scopus 로고    scopus 로고
    • Fractional synchronization of chaotic systems with different orders
    • A. RAZMINIA, D. BALEANU, Fractional synchronization of chaotic systems with different orders, Proc. Romanian Acad. A., 13, pp. 314-321, 2012.
    • (2012) Proc. Romanian Acad. A. , vol.13 , pp. 314-321
    • Razminia, A.1    Baleanu, D.2
  • 21
    • 84877833378 scopus 로고    scopus 로고
    • Fractional calculus analysis of the cosmic microwave background
    • J. A. TENREIRO MACHADO et al., Fractional calculus analysis of the cosmic microwave background, Rom. Rep. Phys., 65, pp. 316-323, 2013.
    • (2013) Rom. Rep. Phys. , vol.65 , pp. 316-323
    • Tenreiro Machado, J.A.1
  • 23
    • 84878993985 scopus 로고    scopus 로고
    • Approximate solutions for diffusion equations on Cantor space-time
    • XIAO-JUN YANG et al., Approximate solutions for diffusion equations on Cantor space-time, Proc. Romanian Acad. A, 14, pp. 127-133, 2013.
    • (2013) Proc. Romanian Acad. A , vol.14 , pp. 127-133
    • Yang, X.1
  • 24
    • 84878434215 scopus 로고    scopus 로고
    • Mean square solutions of second-order random differential equations by using homotopy analysis method
    • A. K. GOLMANKHANEH, N. A. PORGHOVEH, D. BALEANU, Mean square solutions of second-order random differential equations by using homotopy analysis method, Rom. Rep. Phys., 65, pp. 350-362, 2013.
    • (2013) Rom. Rep. Phys. , vol.65 , pp. 350-362
    • Golmankhaneh, A.K.1    Porghoveh, N.A.2    Baleanu, D.3
  • 25
    • 84879528675 scopus 로고    scopus 로고
    • Fractional Euler-Lagrange equation of Caldirola-Kanai oscillator
    • D. BALEANU, J. H. ASAD, I. PETRAS, S. ELAGAN, A. BILGEN, Fractional Euler-Lagrange equation of Caldirola-Kanai oscillator, Rom. Rep. Phys., 64, pp.1171-1177, 2012.
    • (2012) Rom. Rep. Phys. , vol.64 , pp. 1171-1177
    • Baleanu, D.1    Asad, J.H.2    Petras, I.3    Elagan, S.4    Bilgen, A.5
  • 26
    • 84869470751 scopus 로고    scopus 로고
    • Fractional-order two-electric pendulum
    • D. BALEANU, J. H. ASAD, I. PETRAS, Fractional-order two-electric pendulum, Rom. Rep. Phys., 64, pp. 907-914, 2012.
    • (2012) Rom. Rep. Phys. , vol.64 , pp. 907-914
    • Baleanu, D.1    Asad, J.H.2    Petras, I.3
  • 27
    • 84877806817 scopus 로고    scopus 로고
    • Newtonian mechanics on fractals subset of real-line
    • A. K. GOLMANKHANEH et al., Newtonian mechanics on fractals subset of real-line, Rom. Rep. Phys., 65, pp. 84-93, 2013.
    • (2013) Rom. Rep. Phys. , vol.65 , pp. 84-93
    • Golmankhaneh, A.K.1
  • 28
    • 84877270201 scopus 로고    scopus 로고
    • Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis
    • D. ROSTAMY, M. ALIPOUR, H. JAFARI, D. BALEANU, Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis, Rom. Rep. Phys., 65, pp. 334-349, 2013.
    • (2013) Rom. Rep. Phys. , vol.65 , pp. 334-349
    • Rostamy, D.1    Alipour, M.2    Jafari, H.3    Baleanu, D.4
  • 29
    • 84875677289 scopus 로고    scopus 로고
    • Fractional Caputo heat equation within the double Laplace transform
    • A. M. O. ANWAR, F. JARAD, D. BALEANU, F. AYAZ, Fractional Caputo heat equation within the double Laplace transform, Rom. J. Phys., 58, pp. 15-22, 2013.
    • (2013) Rom. J. Phys. , vol.58 , pp. 15-22
    • Anwar, A.M.O.1    Jarad, F.2    Baleanu, D.3    Ayaz, F.4
  • 31
    • 0742323831 scopus 로고    scopus 로고
    • Time-fractional telegraph equations and telegraph processes with brownian time
    • E. ORSINGHER, L. BEGHIN, Time-fractional telegraph equations and telegraph processes with brownian time, Probab. Theor. Rel., 128, pp. 141-160, 2004.
    • (2004) Probab. Theor. Rel. , vol.128 , pp. 141-160
    • Orsingher, E.1    Beghin, L.2
  • 32
    • 34848822538 scopus 로고    scopus 로고
    • Analytical solution for the time-fractional telegraph equation by the method of separating variables
    • J. CHEN, F. LIU, V. ANH, Analytical solution for the time-fractional telegraph equation by the method of separating variables, J. Math. Anal. Appl., 338, pp. 1364-1377, 2008.
    • (2008) J. Math. Anal. Appl. , vol.338 , pp. 1364-1377
    • Chen, J.1    Liu, F.2    Anh, V.3
  • 33
    • 0037254447 scopus 로고    scopus 로고
    • The space-fractional telegraph equation and the related fractional telegraph process
    • E. ORSINGHER, X. ZHAO, The space-fractional telegraph equation and the related fractional telegraph process, Chin. Ann. Math. Ser. B, 24, pp. 45-56, 2003.
    • (2003) Chin. Ann. Math. Ser. B , vol.24 , pp. 45-56
    • Orsingher, E.1    Zhao, X.2
  • 34
    • 27144506208 scopus 로고    scopus 로고
    • Analytic and approximate solutions of the space-and time-fractional telegraph equations
    • S. MOMANI, Analytic and approximate solutions of the space-and time-fractional telegraph equations, Appl. Math. Com., 170, pp. 1126-1134, 2005.
    • (2005) Appl. Math. Com. , vol.170 , pp. 1126-1134
    • Momani, S.1
  • 35
    • 41549101458 scopus 로고    scopus 로고
    • Differentiation to fractional orders and the fractional telegraph equation
    • Article ID 033505
    • R. F. CAMARGO, A. O. CHIACCHIO, E. CAPELAS DE OLIVEIRA, Differentiation to fractional orders and the fractional telegraph equation, J. Math. Phys., 49, Article ID 033505, 2008.
    • (2008) J. Math. Phys. , vol.49
    • Camargo, R.F.1    Chiacchio, A.O.2    De Oliveira, E.C.3
  • 36
    • 78449236821 scopus 로고    scopus 로고
    • Analytical solution for the time-fractional telegraph equation
    • Article ID 890158, 2009
    • F. HUANG, Analytical solution for the time-fractional telegraph equation, J. Appl. Math., 2009, Article ID 890158, 2009.
    • (2009) J. Appl. Math.
    • Huang, F.1
  • 38
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • I. PODLUBNY, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calc. Appl. Anal., 5, pp. 367-386, 2002.
    • (2002) Fract. Calc. Appl. Anal. , vol.5 , pp. 367-386
    • Podlubny, I.1
  • 39
    • 0032136257 scopus 로고    scopus 로고
    • Physical and geometrical interpretation of fractional operators
    • M. MOSHREFI-TORBATI, J.K. HAMMOND, Physical and geometrical interpretation of fractional operators, J. Franklin Inst., 335 B, pp. 1077-1086, 1998.
    • (1998) J. Franklin Inst. , vol.335 B , pp. 1077-1086
    • Moshrefi-Torbati, M.1    Hammond, J.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.