메뉴 건너뛰기




Volumn 7, Issue 5, 2013, Pages 1903-1919

Analytical solutions of fuzzy initial value problems by HAM

Author keywords

Characterization theorem; Fuzzy initial value problems; Homotopy analysis method

Indexed keywords


EID: 84883041146     PISSN: 19350090     EISSN: 23250399     Source Type: Journal    
DOI: 10.12785/amis/070528     Document Type: Article
Times cited : (36)

References (66)
  • 1
    • 0023581045 scopus 로고
    • On the fuzzy initial value problem
    • S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319-330 (1987).
    • (1987) Fuzzy Sets and Systems , vol.24 , pp. 319-330
    • Seikkala, S.1
  • 2
    • 0037411687 scopus 로고    scopus 로고
    • The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology
    • D. P. Datta, The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology, Chaos, Solitons and Fractals, 17, 781-788 (2003).
    • (2003) Chaos, Solitons and Fractals , vol.17 , pp. 781-788
    • Datta, D.P.1
  • 4
    • 18444404944 scopus 로고    scopus 로고
    • From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold
    • M. S. El Naschie, From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold, Chaos, Solitons and Fractals, 25, 969-977 (2005).
    • (2005) Chaos, Solitons and Fractals , vol.25 , pp. 969-977
    • El Naschie, M.S.1
  • 5
    • 18844447784 scopus 로고    scopus 로고
    • Fuzzy modeling and synchronization of hyperchaotic sytems
    • H. Zhang, X. Liao, J. Yu, Fuzzy modeling and synchronization of hyperchaotic sytems, Chaos, Solitons and Fractals, 26, 835-843 (2005).
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 835-843
    • Zhang, H.1    Liao, X.2    Yu, J.3
  • 6
    • 4243058286 scopus 로고    scopus 로고
    • Adaptative control of discrete-time chaotic systems: a fuzzy control approach
    • G. Feng, G. Chen, Adaptative control of discrete-time chaotic systems: a fuzzy control approach, Chaos, Solitons and Fractals, 23, 459-467 (2005).
    • (2005) Chaos, Solitons and Fractals , vol.23 , pp. 459-467
    • Feng, G.1    Chen, G.2
  • 9
    • 0023573517 scopus 로고
    • Fuzzy differential equations
    • O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987).
    • (1987) Fuzzy Sets and Systems , vol.24 , pp. 301-317
    • Kaleva, O.1
  • 10
    • 24944547803 scopus 로고    scopus 로고
    • Bounded solutions for fuzzy differential and integral equations
    • J. J. Nieto, R. Rodríguez-López, Bounded solutions for fuzzy differential and integral equations, Chaos, Solitons and Fractals, 27, 1376-1386 (2006).
    • (2006) Chaos, Solitons and Fractals , vol.27 , pp. 1376-1386
    • Nieto, J.J.1    Rodríguez-López, R.2
  • 11
    • 0037116479 scopus 로고    scopus 로고
    • Toward the theory of fuzzy differential equations
    • D. Vorobiev, S. Seikkala, Toward the theory of fuzzy differential equations, Fuzzy Sets and Systems, 125, 231-237 (2002).
    • (2002) Fuzzy Sets and Systems , vol.125 , pp. 231-237
    • Vorobiev, D.1    Seikkala, S.2
  • 12
    • 0042121384 scopus 로고    scopus 로고
    • Impulsive functional differential inclusions and fuzzy population models
    • M. Guo, X. Xue, R. Li, Impulsive functional differential inclusions and fuzzy population models, Fuzzy Sets and Systems, 138 , 601-615 (2003).
    • (2003) Fuzzy Sets and Systems , vol.138 , pp. 601-615
    • Guo, M.1    Xue, X.2    Li, R.3
  • 14
    • 84863763689 scopus 로고    scopus 로고
    • Solving fuzzy Duffing's equation by the Laplace transform decomposition
    • N. Ahmad, M. Mamat, J. Kavikumar, N. Hamzah, Solving fuzzy Duffing's equation by the Laplace transform decomposition, Applied Mathematical Sciences, 6, 2935-2944 (2012).
    • (2012) Applied Mathematical Sciences , vol.6 , pp. 2935-2944
    • Ahmad, N.1    Mamat, M.2    Kavikumar, J.3    Hamzah, N.4
  • 17
    • 64049113935 scopus 로고    scopus 로고
    • Comparison between some approaches to solve fuzzy differential equations
    • Y. Chalco-Cano, H. Román-Flores, Comparison between some approaches to solve fuzzy differential equations, Fuzzy Sets and Systems, 160, 1517-1527 (2009).
    • (2009) Fuzzy Sets and Systems , vol.160 , pp. 1517-1527
    • Chalco-Cano, Y.1    Román-Flores, H.2
  • 18
    • 34447552426 scopus 로고    scopus 로고
    • Euler polygonal method for metric dynamical systems
    • J. J. Nieto, R. Rodríguez-López, Euler polygonal method for metric dynamical systems, Information Sciences, 177, 587-600 (2007).
    • (2007) Information Sciences , vol.177 , pp. 587-600
    • Nieto, J.J.1    Rodríguez-López, R.2
  • 20
    • 0041110206 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions to the Cauchy problem of fuzzy differential equations
    • S. Song, C. Wu, Existence and uniqueness of solutions to the Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems, 110, 55-67 (2000) .
    • (2000) Fuzzy Sets and Systems , vol.110 , pp. 55-67
    • Song, S.1    Wu, C.2
  • 21
    • 14544296605 scopus 로고    scopus 로고
    • Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations
    • B. Bede, S. G. Gal, Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151, 581-599 (2005
    • (2005) Fuzzy Sets and Systems , vol.151 , pp. 581-599
    • Bede, B.1    Gal, S.G.2
  • 24
    • 4544258343 scopus 로고    scopus 로고
    • Almost periodic fuzzy-number-valued functions
    • B. Bede, S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets and Systems, 147, 385-403 (2004).
    • (2004) Fuzzy Sets and Systems , vol.147 , pp. 385-403
    • Bede, B.1    Gal, S.G.2
  • 25
    • 33846224330 scopus 로고    scopus 로고
    • First order linear fuzzy differential equations under generalized differentiability
    • B. Bede, I. J. Rudas, A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Information Sciences, 177, 1648-1662 (2007).
    • (2007) Information Sciences , vol.177 , pp. 1648-1662
    • Bede, B.1    Rudas, I.J.2    Bencsik, A.L.3
  • 27
    • 68749120554 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential equations under generalized differentiability
    • J. J. Nieto, A. Khastan, K. Ivaz, Numerical solution of fuzzy differential equations under generalized differentiability, Nonlinear Analysis: Hybrid Systems, 3, 700-707 (2009).
    • (2009) Nonlinear Analysis: Hybrid Systems , vol.3 , pp. 700-707
    • Nieto, J.J.1    Khastan, A.2    Ivaz, K.3
  • 28
    • 0000382276 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential equations
    • M. Ma, M. Friedman, A. Kandel, Numerical solution of fuzzy differential equations, Fuzzy Sets and Systems, 105, 133-138 (1999).
    • (1999) Fuzzy Sets and Systems , vol.105 , pp. 133-138
    • Ma, M.1    Friedman, M.2    Kandel, A.3
  • 30
    • 84877941194 scopus 로고    scopus 로고
    • Series solution of fuzzy differential equations under strongly generalized differentiability
    • O. Abu Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, Journal of Advanced Research in Applied Mathematics, 5, 31-52 (2013).
    • (2013) Journal of Advanced Research in Applied Mathematics , vol.5 , pp. 31-52
    • Abu Arqub, O.1
  • 31
    • 58249122332 scopus 로고    scopus 로고
    • Improved predictor-corrector method for solving fuzzy initial value problems
    • T. Allahviranloo, S. Abbasbandy, N. Ahmady, E. Ahmady, Improved predictor-corrector method for solving fuzzy initial value problems, Information Sciences, 179, 945-955 (2009).
    • (2009) Information Sciences , vol.179 , pp. 945-955
    • Allahviranloo, T.1    Abbasbandy, S.2    Ahmady, N.3    Ahmady, E.4
  • 33
    • 75149175056 scopus 로고    scopus 로고
    • Artificial neural network approach for solving fuzzy differential equations
    • S. Effati, M. Pakdaman, Artificial neural network approach for solving fuzzy differential equations, Information Sciences, 180, 1434-1457 (2010).
    • (2010) Information Sciences , vol.180 , pp. 1434-1457
    • Effati, S.1    Pakdaman, M.2
  • 35
    • 84867025265 scopus 로고    scopus 로고
    • Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integro-differential equations
    • O. Abu Arqub, M. Al-Smadi, S. Momani, Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integro-differential equations, Abstract and Applied Analysis, 2012, 16 (2012).
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 16
    • Abu Arqub, O.1    Al-Smadi, M.2    Momani, S.3
  • 36
    • 84871437077 scopus 로고    scopus 로고
    • Solving singular two-point boundary value problems using continuous genetic algorithm
    • O. Abu Arqub, Z. Abo Hammour, S. Momani, Solving singular two-point boundary value problems using continuous genetic algorithm, Abstract and Applied Analysis, 2012, 25 (2012).
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 25
    • Abu Arqub, O.1    Abo Hammour, Z.2    Momani, S.3
  • 37
    • 84863773713 scopus 로고    scopus 로고
    • Approximate solution of BVPs for 4th-order IDEs by using RKHS method
    • M. Al-Smadi, O. Abu Arqub, N. Shawagfeh, Approximate solution of BVPs for 4th-order IDEs by using RKHS method, Applied Mathematical Sciences, 6, 2453-2464 (2012).
    • (2012) Applied Mathematical Sciences , vol.6 , pp. 2453-2464
    • Al-Smadi, M.1    Abu Arqub, O.2    Shawagfeh, N.3
  • 38
    • 84882995268 scopus 로고    scopus 로고
    • Linear Fractional Time Minimizing Transportation Problem with Impurities
    • Madhuri, Linear Fractional Time Minimizing Transportation Problem with Impurities, Information Sciences Letters, 1, 7-19 (2012).
    • (2012) Information Sciences Letters , vol.1 , pp. 7-19
    • Madhuri1
  • 40
    • 84876512794 scopus 로고    scopus 로고
    • New Class of Boundary Value Problems
    • A. Atangana, New Class of Boundary Value Problems, Information Sciences Letters, 1, 67-76 (2012).
    • (2012) Information Sciences Letters , vol.1 , pp. 67-76
    • Atangana, A.1
  • 41
    • 84882988835 scopus 로고    scopus 로고
    • Boundary gradient observability for semilinear parabolic systems: Sectorial approach
    • B. Ali, Boundary gradient observability for semilinear parabolic systems: Sectorial approach, Mathematical Sciences Letters, 2, 45-54 (2013).
    • (2013) Mathematical Sciences Letters , vol.2 , pp. 45-54
    • Ali, B.1
  • 43
    • 0141961626 scopus 로고    scopus 로고
    • On the homotopy analysis method for nonlinear problems
    • S. J. Liao, On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computationm, 147, 499-513 (2004).
    • (2004) Applied Mathematics and Computationm , vol.147 , pp. 499-513
    • Liao, S.J.1
  • 44
    • 0032285655 scopus 로고    scopus 로고
    • Homotopy analysis method: A new analytic method for nonlinear problems
    • S. J. Liao, Homotopy analysis method: A new analytic method for nonlinear problems, Applied Mathematics and Mechanics, 19, 957-962 (1998).
    • (1998) Applied Mathematics and Mechanics , vol.19 , pp. 957-962
    • Liao, S.J.1
  • 45
    • 0037300634 scopus 로고    scopus 로고
    • Homotopy analysis method of nonlinear progressive waves in deep water
    • S. J. Liao, K. F. Cheung, Homotopy analysis method of nonlinear progressive waves in deep water, Journal of Engineering Mathematics, 45, 105-116 (2003).
    • (2003) Journal of Engineering Mathematics , vol.45 , pp. 105-116
    • Liao, S.J.1    Cheung, K.F.2
  • 46
    • 33748300795 scopus 로고    scopus 로고
    • Series solutions of unsteady boundary-layer flows over a stretching flat plate
    • S. J. Liao, Series solutions of unsteady boundary-layer flows over a stretching flat plate, Studies in Applied Mathematics, 117, 239-263 (2006).
    • (2006) Studies in Applied Mathematics , vol.117 , pp. 239-263
    • Liao, S.J.1
  • 47
    • 17644421077 scopus 로고    scopus 로고
    • Solving solitary waves with discontinuity by means of the homotopy analysis method
    • W.Wu, S. J. Liao, Solving solitary waves with discontinuity by means of the homotopy analysis method, Chaos, Solitons and Fractals, 26, 177-185 (2005) .
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 177-185
    • Wu, W.1    Liao, S.J.2
  • 48
    • 27144505139 scopus 로고    scopus 로고
    • Solving the Klein-Gordon equation by means of the homotopy analysis method
    • Q. Sun, Solving the Klein-Gordon equation by means of the homotopy analysis method, Applied Mathematics and Computation, 169, 355-365 (2005).
    • (2005) Applied Mathematics and Computation , vol.169 , pp. 355-365
    • Sun, Q.1
  • 49
    • 84867790334 scopus 로고    scopus 로고
    • Homotopy analysis method for second-order boundary value problems of integro-differential equations
    • A. El-Ajou, O. Abu Arqub, S. Momani, Homotopy analysis method for second-order boundary value problems of integro-differential equations, Discrete Dynamics in Nature and Society, 2012, 18 (2012).
    • (2012) Discrete Dynamics in Nature and Society , vol.2012 , pp. 18
    • El-Ajou, A.1    Abu Arqub, O.2    Momani, S.3
  • 50
    • 69249202653 scopus 로고    scopus 로고
    • The homotopy analysis method for handling systems of fractional differential equations
    • M. Zurigat, S. Momani, Z. Odibat, A. Alawneh, The homotopy analysis method for handling systems of fractional differential equations, Applied Mathematical Modelling, 34, 24-35 (2010).
    • (2010) Applied Mathematical Modelling , vol.34 , pp. 24-35
    • Zurigat, M.1    Momani, S.2    Odibat, Z.3    Alawneh, A.4
  • 51
    • 70350378693 scopus 로고    scopus 로고
    • A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations
    • Z. Odibat, S. Momani, H. Xu, A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations, AppliedMathematicalModelling, 34, 593-600 (2010).
    • (2010) AppliedMathematicalModelling , vol.34 , pp. 593-600
    • Odibat, Z.1    Momani, S.2    Xu, H.3
  • 53
    • 74149089078 scopus 로고    scopus 로고
    • Analytical approximate solutions of systems of fractional algebraicdifferential equations by homotopy analysis method
    • M. Zurigat, S. Momani, A. Alawneh, Analytical approximate solutions of systems of fractional algebraicdifferential equations by homotopy analysis method, Computers & Mathematics with Applications, 59, 1227-1235 (2010).
    • (2010) Computers & Mathematics with Applications , vol.59 , pp. 1227-1235
    • Zurigat, M.1    Momani, S.2    Alawneh, A.3
  • 54
    • 84871119609 scopus 로고    scopus 로고
    • Solution of the fractional epidemic model by Homotopy analysis method
    • O. Abu Arqub, A. El-Ajou, Solution of the fractional epidemic model by Homotopy analysis method, Journal of King Saud University (Science), 25, 73-81 (2013) .
    • (2013) Journal of King Saud University (Science) , vol.25 , pp. 73-81
    • Abu Arqub, O.1    El-Ajou, A.2
  • 55
    • 84883015683 scopus 로고    scopus 로고
    • Effect of MHD and Thermal Diffusion on Natural Convection Oscillatory Flow Past Plate with Viscous Heating
    • P. K. Sharma, Chhama Singh, Effect of MHD and Thermal Diffusion on Natural Convection Oscillatory Flow Past Plate with Viscous Heating,Mathematical Sciences Letters, 2, 79-86 (2013)
    • (2013) Mathematical Sciences Letters , vol.2 , pp. 79-86
    • Sharma, P.K.1    Singh, C.2
  • 60
    • 0004869884 scopus 로고    scopus 로고
    • Attractors and asymptotic stability for fuzzy dynamical systems
    • R. C. Bassanezi, L. C. de Barros, P. A. Tonelli, Attractors and asymptotic stability for fuzzy dynamical systems, Fuzzy Sets and Systems, 113, 473-483 (2000).
    • (2000) Fuzzy Sets and Systems , vol.113 , pp. 473-483
    • Bassanezi, R.C.1    de Barros, L.C.2    Tonelli, P.A.3
  • 63
    • 76049117931 scopus 로고    scopus 로고
    • An optiomal homotopy-analysis approach for strongly nonlinear differential equation
    • S. J. Liao, An optiomal homotopy-analysis approach for strongly nonlinear differential equation, Communications in Nonlinear Science and Numerical Simulation, 15, 2003-2016 (2010).
    • (2010) Communications in Nonlinear Science and Numerical Simulation , vol.15 , pp. 2003-2016
    • Liao, S.J.1
  • 64
    • 64549148828 scopus 로고    scopus 로고
    • Series solutions of nonlinear Riccati differential equations with fractional order
    • J. Cang, Y. Tan, H. Xu, S. J. Liao, Series solutions of nonlinear Riccati differential equations with fractional order, Chaos, Solitons and Fractals, 40, 1-9 (2009).
    • (2009) Chaos, Solitons and Fractals , vol.40 , pp. 1-9
    • Cang, J.1    Tan, Y.2    Xu, H.3    Liao, S.J.4
  • 65
    • 34249806325 scopus 로고    scopus 로고
    • Derivation of the Adomian decomposition method using the homotopy analysis method
    • F. M. Allan, Derivation of the Adomian decomposition method using the homotopy analysis method, Applied Mathematics and Computation, 190, 6-14 (2007).
    • (2007) Applied Mathematics and Computation , vol.190 , pp. 6-14
    • Allan, F.M.1
  • 66
    • 25844456083 scopus 로고    scopus 로고
    • Comparison between the homotopy analysis method and homotopy perturbation method
    • S. J. Liao, Comparison between the homotopy analysis method and homotopy perturbation method, Applied Mathematics and Computation, 169, 1186-1194 (2005).
    • (2005) Applied Mathematics and Computation , vol.169 , pp. 1186-1194
    • Liao, S.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.