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Volumn 217, Issue 5, 2010, Pages 2162-2168

A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation

Author keywords

Caputo fractional derivative; Existence and uniqueness; Fractional order differential equations; Initial value problems; Interval analysis; Validated computing

Indexed keywords

CAPUTO FRACTIONAL DERIVATIVES; EXISTENCE AND UNIQUENESS; FRACTIONAL ORDER; INITIAL VALUES; INTERVAL ANALYSIS; VALIDATED COMPUTING;

EID: 77957308442     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.07.015     Document Type: Article
Times cited : (21)

References (29)
  • 1
    • 77953332285 scopus 로고    scopus 로고
    • Applications of fractional calculus
    • M. Dalir, and M. Bashour Applications of fractional calculus Applied Mathematical Sciences 4 21 2010 1021 1032
    • (2010) Applied Mathematical Sciences , vol.4 , Issue.21 , pp. 1021-1032
    • Dalir, M.1    Bashour, M.2
  • 3
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent-II
    • M. Caputo Linear models of dissipation whose Q is almost frequency independent-II Geophysical Journal International 13 5 1967 529 539
    • (1967) Geophysical Journal International , vol.13 , Issue.5 , pp. 529-539
    • Caputo, M.1
  • 4
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • D. Delbosco, and L. Rodino Existence and uniqueness for a nonlinear fractional differential equation Journal of Mathematical Analysis and Applications 204 2 1996 609 625
    • (1996) Journal of Mathematical Analysis and Applications , vol.204 , Issue.2 , pp. 609-625
    • Delbosco, D.1    Rodino, L.2
  • 6
    • 33244471191 scopus 로고    scopus 로고
    • An extension of Picard-Lindeloff theorem to fractional differential equations
    • N. Hayek, J. Trujillo, M. Rivero, B. Bonilla, and J. Moreno An extension of Picard-Lindeloff theorem to fractional differential equations Applicable Analysis 70 3-4 1999 347 361
    • (1999) Applicable Analysis , vol.70 , Issue.34 , pp. 347-361
    • Hayek, N.1    Trujillo, J.2    Rivero, M.3    Bonilla, B.4    Moreno, J.5
  • 8
    • 53949111458 scopus 로고    scopus 로고
    • Basic theory of fractional differential equations
    • V. Lakshmikantham, and A. Vatsala Basic theory of fractional differential equations Nonlinear Analysis 69 8 2008 2677 2682
    • (2008) Nonlinear Analysis , vol.69 , Issue.8 , pp. 2677-2682
    • Lakshmikantham, V.1    Vatsala, A.2
  • 9
    • 74149092121 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions for a system of fractional differential equations
    • Y. Zhou Existence and uniqueness of solutions for a system of fractional differential equations Fractional Calculus & Applied Analysis 12 2 2009 195 204
    • (2009) Fractional Calculus & Applied Analysis , vol.12 , Issue.2 , pp. 195-204
    • Zhou, Y.1
  • 10
    • 77950188013 scopus 로고    scopus 로고
    • Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
    • J. Deng, and L. Ma Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations Applied Mathematics Letters 23 6 2010 676 680
    • (2010) Applied Mathematics Letters , vol.23 , Issue.6 , pp. 676-680
    • Deng, J.1    Ma, L.2
  • 12
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • F. Mainardi, Y. Luchko, and G. Pagnini The fundamental solution of the space-time fractional diffusion equation Fractional Calculus and Applied Analysis 4 2 2001 153 192
    • (2001) Fractional Calculus and Applied Analysis , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 13
    • 33746218471 scopus 로고    scopus 로고
    • Solving a system of nonlinear fractional differential equations using Adomian decomposition
    • DOI 10.1016/j.cam.2005.10.017, PII S0377042705006278
    • H. Jafari, and V. Daftardar-Gejji Solving a system of nonlinear fractional differential equations using Adomian decomposition Journal of Computational and Applied Mathematics 196 2 2006 644 651 (Pubitemid 44093887)
    • (2006) Journal of Computational and Applied Mathematics , vol.196 , Issue.2 , pp. 644-651
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 14
    • 35348869861 scopus 로고    scopus 로고
    • Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
    • Z. Odibat, and S. Momani Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order Chaos, Solitons and Fractals 36 1 2008 167 174
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.1 , pp. 167-174
    • Odibat, Z.1    Momani, S.2
  • 15
    • 64549148828 scopus 로고    scopus 로고
    • Series solutions of nonlinear Riccati differential equations with fractional order
    • J. Cang, Y. Tan, H. Xu, and S. Liao Series solutions of nonlinear Riccati differential equations with fractional order Chaos, Solitons and Fractals 40 1 2009 1 9
    • (2009) Chaos, Solitons and Fractals , vol.40 , Issue.1 , pp. 1-9
    • Cang, J.1    Tan, Y.2    Xu, H.3    Liao, S.4
  • 16
    • 34250215244 scopus 로고    scopus 로고
    • Solution of fractional differential equations by using differential transform method
    • A. Arikoglu, and I. Ozkol Solution of fractional differential equations by using differential transform method Chaos, Solitons and Fractals 34 5 2007 1473 1481
    • (2007) Chaos, Solitons and Fractals , vol.34 , Issue.5 , pp. 1473-1481
    • Arikoglu, A.1    Ozkol, I.2
  • 17
    • 47849126401 scopus 로고    scopus 로고
    • A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
    • S. Momani, and Z. Odibat A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylor's formula Journal of Computational and Applied Mathematics 220 1-2 2008 85 95
    • (2008) Journal of Computational and Applied Mathematics , vol.220 , Issue.12 , pp. 85-95
    • Momani, S.1    Odibat, Z.2
  • 18
    • 39449122795 scopus 로고    scopus 로고
    • Generalized differential transform method: Application to differential equations of fractional order
    • DOI 10.1016/j.amc.2007.07.068, PII S0096300307007916
    • Z. Odibat, S. Momani, and V. Erturk Generalized differential transform method: application to differential equations of fractional order Applied Mathematics and Computation 197 2 2008 467 477 (Pubitemid 351273764)
    • (2008) Applied Mathematics and Computation , vol.197 , Issue.2 , pp. 467-477
    • Odibat, Z.1    Momani, S.2    Erturk, V.S.3
  • 19
    • 30344464250 scopus 로고    scopus 로고
    • Application of variational iteration method to nonlinear differential equations of fractional order
    • Z. Odibat, and S. Momani Application of variational iteration method to nonlinear differential equations of fractional order International Journal of Nonlinear Sciences and Numerical Simulation 7 1 2006 27 34
    • (2006) International Journal of Nonlinear Sciences and Numerical Simulation , vol.7 , Issue.1 , pp. 27-34
    • Odibat, Z.1    Momani, S.2
  • 20
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • DOI 10.1023/A:1016592219341, Fractional Order Calculus and Its Applications
    • K. Diethelm, N. Ford, and A. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 1 2002 3 22 (Pubitemid 34945390)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 21
    • 3042709180 scopus 로고    scopus 로고
    • Multi-order fractional differential equations and their numerical solution
    • K. Diethelm, and N. Ford Multi-order fractional differential equations and their numerical solution Applied Mathematics and Computation 154 3 2004 621 640
    • (2004) Applied Mathematics and Computation , vol.154 , Issue.3 , pp. 621-640
    • Diethelm, K.1    Ford, N.2
  • 22
  • 23
    • 34047210346 scopus 로고    scopus 로고
    • Validated solutions of initial value problems for parametric ODEs
    • Y. Lin, and M. Stadtherr Validated solutions of initial value problems for parametric ODEs Applied Numerical Mathematics 57 10 2007 1145 1162
    • (2007) Applied Numerical Mathematics , vol.57 , Issue.10 , pp. 1145-1162
    • Lin, Y.1    Stadtherr, M.2
  • 25
    • 0002265766 scopus 로고    scopus 로고
    • Validated solutions of initial value problems for ordinary differential equations
    • N. Nedialkov, K. Jackson, and G. Corliss Validated solutions of initial value problems for ordinary differential equations Applied Mathematics and Computation 105 1 1999 21 68
    • (1999) Applied Mathematics and Computation , vol.105 , Issue.1 , pp. 21-68
    • Nedialkov, N.1    Jackson, K.2    Corliss, G.3
  • 28
    • 34250093591 scopus 로고
    • Inclusion functions and global optimization II
    • R. Moore, and H. Ratschek Inclusion functions and global optimization II Mathematical Programming 41 1 1988 341 356
    • (1988) Mathematical Programming , vol.41 , Issue.1 , pp. 341-356
    • Moore, R.1    Ratschek, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.