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Volumn 2013, Issue , 2013, Pages

On solutions of linear fractional differential equations with uncertainty

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EID: 84890018705     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/178378     Document Type: Article
Times cited : (10)

References (38)
  • 1
    • 84880877553 scopus 로고    scopus 로고
    • A Jacobi operational matrix for solving a fuzzy linear fractional differential equation
    • 10.1186/1687-1847-2013-104
    • Ahmadian A., Suleiman M., Salahshour S., Baleanu D., A Jacobi operational matrix for solving a fuzzy linear fractional differential equation. Advances in Difference Equations 2013 2013, article 104 1 29 10.1186/1687-1847-2013-104
    • (2013) Advances in Difference Equations , pp. 1-29
    • Ahmadian, A.1    Suleiman, M.2    Salahshour, S.3    Baleanu, D.4
  • 2
    • 70350649223 scopus 로고    scopus 로고
    • Fuzzy Laplace transforms
    • 2-s2.0-70350649223 10.1007/s00500-008-0397-6
    • Allahviranloo T., Ahmadi M. B., Fuzzy Laplace transforms. Soft Computing 2010 14 3 235 243 2-s2.0-70350649223 10.1007/s00500-008-0397-6
    • (2010) Soft Computing , vol.14 , Issue.3 , pp. 235-243
    • Allahviranloo, T.1    Ahmadi, M.B.2
  • 3
    • 84855651248 scopus 로고    scopus 로고
    • Explicit solutions of fractional differential equations with uncertainty
    • 2-s2.0-84855651248 10.1007/s00500-011-0743-y
    • Allahviranloo T., Salahshour S., Abbasbandy S., Explicit solutions of fractional differential equations with uncertainty. Soft Computing 2012 16 2 297 302 2-s2.0-84855651248 10.1007/s00500-011-0743-y
    • (2012) Soft Computing , vol.16 , Issue.2 , pp. 297-302
    • Allahviranloo, T.1    Salahshour, S.2    Abbasbandy, S.3
  • 4
    • 79959550117 scopus 로고    scopus 로고
    • A new method for solving fuzzy linear differential equations
    • 10.1007/s00607-010-0136-6 MR2794923
    • Allahviranloo T., Abbasbandy S., Salahshour S., Hakimzadeh A., A new method for solving fuzzy linear differential equations. Computing 2011 92 2 181 197 10.1007/s00607-010-0136-6 MR2794923
    • (2011) Computing , vol.92 , Issue.2 , pp. 181-197
    • Allahviranloo, T.1    Abbasbandy, S.2    Salahshour, S.3    Hakimzadeh, A.4
  • 6
    • 84861102043 scopus 로고    scopus 로고
    • The Cauchy problem of fuzzy differential equations under generalized differentiability
    • 10.1016/j.fss.2011.10.009 MR2927841
    • Li J., Zhao A., Yan J., The Cauchy problem of fuzzy differential equations under generalized differentiability. Fuzzy Sets and Systems 2012 200 1 24 10.1016/j.fss.2011.10.009 MR2927841
    • (2012) Fuzzy Sets and Systems , vol.200 , pp. 1-24
    • Li, J.1    Zhao, A.2    Yan, J.3
  • 7
    • 84870248876 scopus 로고    scopus 로고
    • Application of fuzzy differential transform method for solving fuzzy Volterra integral equations
    • 10.1016/j.apm.2012.03.031 MR3002203
    • Salahshour S., Allahviranloo T., Application of fuzzy differential transform method for solving fuzzy Volterra integral equations. Applied Mathematical Modelling 2013 37 3 1016 1027 10.1016/j.apm.2012.03.031 MR3002203
    • (2013) Applied Mathematical Modelling , vol.37 , Issue.3 , pp. 1016-1027
    • Salahshour, S.1    Allahviranloo, T.2
  • 8
    • 84871935994 scopus 로고    scopus 로고
    • Applications of fuzzy Laplace transforms
    • 10.1007/s00500-012-0907-4
    • Salahshour S., Allahviranloo A., Applications of fuzzy Laplace transforms. Soft Computing 2013 17 1 145 178 10.1007/s00500-012-0907-4
    • (2013) Soft Computing , vol.17 , Issue.1 , pp. 145-178
    • Salahshour, S.1    Allahviranloo, A.2
  • 11
    • 0002355788 scopus 로고
    • On the fractional order initial value problem and its engineering applications
    • Tokyo, Japan College of Engineering, Nihon University
    • Bagley R. L., Nishimoto K., On the fractional order initial value problem and its engineering applications. Fractional Calculus and Its Applications 1990 Tokyo, Japan College of Engineering, Nihon University 12 20
    • (1990) Fractional Calculus and Its Applications , pp. 12-20
    • Bagley, R.L.1    Nishimoto, K.2
  • 12
    • 84981825145 scopus 로고
    • Definition of physically consistent damping laws with fractional derivatives
    • 10.1002/zamm.19950750820 MR1347683
    • Beyer H., Kempfle S., Definition of physically consistent damping laws with fractional derivatives. Zeitschrift für Angewandte Mathematik und Mechanik 1995 75 8 623 635 10.1002/zamm.19950750820 MR1347683
    • (1995) Zeitschrift für Angewandte Mathematik und Mechanik , vol.75 , Issue.8 , pp. 623-635
    • Beyer, H.1    Kempfle, S.2
  • 13
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • 10.1006/jmaa.2000.7194 MR1876137
    • Diethelm K., Ford N. J., Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications 2002 265 2 229 248 10.1006/jmaa.2000.7194 MR1876137
    • (2002) Journal of Mathematical Analysis and Applications , vol.265 , Issue.2 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 14
    • 0003797958 scopus 로고    scopus 로고
    • San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022
    • Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 18
    • 53949111458 scopus 로고    scopus 로고
    • Basic theory of fractional differential equations
    • 10.1016/j.na.2007.08.042 MR2446361
    • Lakshmikantham V., Vatsala A. S., Basic theory of fractional differential equations. Nonlinear Analysis: Theory, Methods & Applications 2008 69 8 2677 2682 10.1016/j.na.2007.08.042 MR2446361
    • (2008) Nonlinear Analysis: Theory, Methods & Applications , vol.69 , Issue.8 , pp. 2677-2682
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 19
    • 73249139676 scopus 로고    scopus 로고
    • On the concept of solution for fractional differential equations with uncertainty
    • 10.1016/j.na.2009.11.029 MR2580143
    • Agarwal R. P., Lakshmikantham V., Nieto J. J., On the concept of solution for fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods & Applications 2010 72 6 2859 2862 10.1016/j.na.2009.11.029 MR2580143
    • (2010) Nonlinear Analysis: Theory, Methods & Applications , vol.72 , Issue.6 , pp. 2859-2862
    • Agarwal, R.P.1    Lakshmikantham, V.2    Nieto, J.J.3
  • 20
    • 14544296605 scopus 로고    scopus 로고
    • Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
    • DOI 10.1016/j.fss.2004.08.001, PII S0165011404003173
    • Bede B., Gal S. G., Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems 2005 151 3 581 599 10.1016/j.fss.2004.08.001 MR2126175 (Pubitemid 40305079)
    • (2005) Fuzzy Sets and Systems , vol.151 , Issue.3 , pp. 581-599
    • Bede, B.1    Gal, S.G.2
  • 21
    • 33846224330 scopus 로고    scopus 로고
    • First order linear fuzzy differential equations under generalized differentiability
    • DOI 10.1016/j.ins.2006.08.021, PII S0020025506002611, Fuzzy set applications in Industrial Engineering
    • Bede B., Rudas I. J., Bencsik A. L., First order linear fuzzy differential equations under generalized differentiability. Information Sciences 2007 177 7 1648 1662 10.1016/j.ins.2006.08.021 MR2303177 (Pubitemid 46107427)
    • (2007) Information Sciences , vol.177 , Issue.7 , pp. 1648-1662
    • Bede, B.1    Rudas, I.J.2    Bencsik, A.L.3
  • 22
    • 33644989946 scopus 로고    scopus 로고
    • Fuzzy transforms: Theory and applications
    • 10.1016/j.fss.2005.11.012 MR2218243
    • Perfilieva I., Fuzzy transforms: theory and applications. Fuzzy Sets and Systems 2006 157 8 993 1023 10.1016/j.fss.2005.11.012 MR2218243
    • (2006) Fuzzy Sets and Systems , vol.157 , Issue.8 , pp. 993-1023
    • Perfilieva, I.1
  • 24
    • 84878639673 scopus 로고    scopus 로고
    • Existence and uniqueness results for fractional differential equations with uncertainty
    • 10.1186/1687-1847-2012-112 MR3015434
    • Salahshour S., Allahviranloo T., Abbasbandy S., Baleanu D., Existence and uniqueness results for fractional differential equations with uncertainty. Advances in Difference Equations 2012 2012, article 112 1 12 10.1186/1687-1847-2012-112 MR3015434
    • (2012) Advances in Difference Equations , pp. 1-12
    • Salahshour, S.1    Allahviranloo, T.2    Abbasbandy, S.3    Baleanu, D.4
  • 25
    • 84865638623 scopus 로고    scopus 로고
    • Modified fractional Euler method for solving fuzzy fractional initial value problem
    • 10.1016/j.cnsns.2012.06.008 MR2974357
    • Mazandarani M., Kamyad A. V., Modified fractional Euler method for solving fuzzy fractional initial value problem. Communications in Nonlinear Science and Numerical Simulation 2013 18 1 12 21 10.1016/j.cnsns.2012.06.008 MR2974357
    • (2013) Communications in Nonlinear Science and Numerical Simulation , vol.18 , Issue.1 , pp. 12-21
    • Mazandarani, M.1    Kamyad, A.V.2
  • 26
    • 84869161109 scopus 로고    scopus 로고
    • Fuzzy fractional integral equations under compactness type condition
    • 10.2478/s13540-012-0040-1 MR2974320
    • Agarwal R. P., Arshad S., O'Regan D., Lupulescu V., Fuzzy fractional integral equations under compactness type condition. Fractional Calculus and Applied Analysis 2012 15 4 572 590 10.2478/s13540-012-0040-1 MR2974320
    • (2012) Fractional Calculus and Applied Analysis , vol.15 , Issue.4 , pp. 572-590
    • Agarwal, R.P.1    Arshad, S.2    O'Regan, D.3    Lupulescu, V.4
  • 27
    • 34548156679 scopus 로고    scopus 로고
    • A class of linear differential dynamical systems with fuzzy initial condition
    • DOI 10.1016/j.fss.2007.04.016, PII S0165011407001972
    • Xu J., Liao Z., Hu Z., A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Sets and Systems 2007 158 21 2339 2358 10.1016/j.fss.2007.04.016 MR2360320 (Pubitemid 47313536)
    • (2007) Fuzzy Sets and Systems , vol.158 , Issue.21 , pp. 2339-2358
    • Xu, J.1    Liao, Z.2    Hu, Z.3
  • 28
    • 0009933836 scopus 로고    scopus 로고
    • Numerical solutions of fuzzy differential and integral equations
    • PII S0165011498003558, Fuzzy Modeling and Dynamics
    • Friedman M., Ma M., Kandel A., Numerical solutions of fuzzy differential and integral equations. Fuzzy Sets and Systems 1999 106 1 35 48 10.1016/S0165-0114(98)00355-8 MR1689568 (Pubitemid 129524548)
    • (1999) Fuzzy Sets and Systems , vol.106 , Issue.1 , pp. 35-48
    • Friedman, M.1    Ma, M.2    Kandel, A.3
  • 29
    • 0000382276 scopus 로고    scopus 로고
    • Numerical solutions of fuzzy differential equations
    • PII S0165011497002339
    • Ma M., Friedman M., Kandel A., Numerical solutions of fuzzy differential equations. Fuzzy Sets and Systems 1999 105 1 133 138 10.1016/S0165-0114(97) 00233-9 MR1688006 (Pubitemid 129523994)
    • (1999) Fuzzy Sets and Systems , vol.105 , Issue.1 , pp. 133-138
    • Ma, M.1    Friedman, M.2    Kandel, A.3
  • 32
    • 0032202946 scopus 로고    scopus 로고
    • The improper fuzzy Riemann integral and its numerical integration
    • PII S0020025598000164
    • Wu H.-C., The improper fuzzy Riemann integral and its numerical integration. Information Sciences 1998 111 1-4 109 137 10.1016/S0020-0255(98) 00016-4 MR1649896 (Pubitemid 128383891)
    • (1998) Information Sciences , vol.111 , Issue.1-4 , pp. 109-137
    • Wu, H.-C.1
  • 33
    • 77950158382 scopus 로고    scopus 로고
    • Berlin, Germany Springer Studies in Fuzziness and Soft Computing 10.1007/978-3-642-11220-1 MR2759224
    • Anastassiou G. A., Fuzzy Mathematics: Approximation Theory 2010 251 Berlin, Germany Springer Studies in Fuzziness and Soft Computing 10.1007/978-3-642-11220-1 MR2759224
    • (2010) Fuzzy Mathematics: Approximation Theory , vol.251
    • Anastassiou, G.A.1
  • 34
    • 84885442325 scopus 로고    scopus 로고
    • Berlin, Germany Springer Intelligent Systems Reference Library 10.1007/978-3-642-17098-0 MR2905440
    • Anastassiou G. A., Intelligent Mathematics: Computational Analysis 2011 5 Berlin, Germany Springer xviii+802 Intelligent Systems Reference Library 10.1007/978-3-642-17098-0 MR2905440
    • (2011) Intelligent Mathematics: Computational Analysis , vol.5
    • Anastassiou, G.A.1
  • 36
    • 41849120488 scopus 로고    scopus 로고
    • On new solutions of fuzzy differential equations
    • DOI 10.1016/j.chaos.2006.10.043, PII S0960077906010241
    • Chalco-Cano Y., Román-Flores H., On new solutions of fuzzy differential equations. Chaos, Solitons and Fractals 2008 38 1 112 119 10.1016/j.chaos.2006.10.043 MR2417648 (Pubitemid 351503972)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.1 , pp. 112-119
    • Chalco-Cano, Y.1    Roman-Flores, H.2
  • 37
    • 79958159192 scopus 로고    scopus 로고
    • Variation of constant formula for first order fuzzy differential equations
    • 10.1016/j.fss.2011.02.020 MR2812829
    • Khastan A., Nieto J. J., Rodríguez-López R., Variation of constant formula for first order fuzzy differential equations. Fuzzy Sets and Systems 2011 177 20 33 10.1016/j.fss.2011.02.020 MR2812829
    • (2011) Fuzzy Sets and Systems , vol.177 , pp. 20-33
    • Khastan, A.1    Nieto, J.J.2    Rodríguez-López, R.3
  • 38
    • 84870067035 scopus 로고    scopus 로고
    • Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability
    • 10.1016/j.ins.2012.07.057 MR2998530
    • Khastan A., Nieto J. J., Rodríguez-López R., Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability. Information Sciences 2013 222 544 558 10.1016/j.ins.2012.07.057 MR2998530
    • (2013) Information Sciences , vol.222 , pp. 544-558
    • Khastan, A.1    Nieto, J.J.2    Rodríguez-López, R.3


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