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Volumn 55, Issue 3-4, 2012, Pages 1106-1117

Solution existence for non-autonomous variable-order fractional differential equations

Author keywords

Fractional calculus; Functional analysis; Solution existence; Variable order fractional differential equation

Indexed keywords

BASIC CONCEPTS; CONSTANT ORDERS; EXISTENCE AND UNIQUENESS; FRACTIONAL CALCULUS; FRACTIONAL DIFFERENTIAL EQUATIONS; LEBESGUE; NONAUTONOMOUS; NONLINEAR TERMS; SEQUENTIAL DERIVATIVES; SOLUTION EXISTENCE; VARIABLE ORDER;

EID: 84855203375     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.09.034     Document Type: Article
Times cited : (91)

References (40)
  • 3
    • 36348976811 scopus 로고    scopus 로고
    • Fractional calculus: a mathematical tool from the past for the present engineer
    • Cafagna D. Fractional calculus: a mathematical tool from the past for the present engineer. IEEE Transactions on Industrial Electronic 2007, 35-40.
    • (2007) IEEE Transactions on Industrial Electronic , pp. 35-40
    • Cafagna, D.1
  • 4
    • 70350366353 scopus 로고    scopus 로고
    • Brownian and fractional Brownian stochastic currents via Malliavin calculus
    • Flandoli F., Tudor C.A. Brownian and fractional Brownian stochastic currents via Malliavin calculus. Journal of Functional Analysis 2010, 258:279-306.
    • (2010) Journal of Functional Analysis , vol.258 , pp. 279-306
    • Flandoli, F.1    Tudor, C.A.2
  • 5
    • 33745082228 scopus 로고    scopus 로고
    • New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations
    • Jumarie G. New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations. Mathematical and Computer Modelling 2006, 44:231-254.
    • (2006) Mathematical and Computer Modelling , vol.44 , pp. 231-254
    • Jumarie, G.1
  • 7
    • 62949246184 scopus 로고    scopus 로고
    • Inversion of the Kipriyanov-radon transform via fractional derivatives in a one dimensional parameter
    • Lyakhov L.N., Gots G. Inversion of the Kipriyanov-radon transform via fractional derivatives in a one dimensional parameter. Journal of Mathematical Sciences 2009, 158:235-240.
    • (2009) Journal of Mathematical Sciences , vol.158 , pp. 235-240
    • Lyakhov, L.N.1    Gots, G.2
  • 8
    • 69849102987 scopus 로고    scopus 로고
    • On one class of differential equations of fractional order
    • Vityuk A.N., Mikhailenko A.V. On one class of differential equations of fractional order. Nonlinear Oscillations 2008, 11:307-319.
    • (2008) Nonlinear Oscillations , vol.11 , pp. 307-319
    • Vityuk, A.N.1    Mikhailenko, A.V.2
  • 9
    • 68649098514 scopus 로고    scopus 로고
    • Variable-order fractional differential operators in anomalous diffusion modeling
    • Sun HongGuang, Chen Wen, Chen YangQuan Variable-order fractional differential operators in anomalous diffusion modeling. Physica A 2009, 388:4586-4592.
    • (2009) Physica A , vol.388 , pp. 4586-4592
    • Sun, H.1    Chen, W.2    Chen, Y.3
  • 10
    • 0346897985 scopus 로고    scopus 로고
    • Mechanics with variable-order differential operators
    • Coimbra C.F.M. Mechanics with variable-order differential operators. Annalen der Physik 2003, 12:692-703.
    • (2003) Annalen der Physik , vol.12 , pp. 692-703
    • Coimbra, C.F.M.1
  • 11
    • 79952043566 scopus 로고    scopus 로고
    • Synthesis of multifractional Gaussian noises based on variable-order fractional operators
    • Sheng Hu, Sun Hongguang, Chen YangQuan, Qiu TianShuang Synthesis of multifractional Gaussian noises based on variable-order fractional operators. Signal Processing 2011, 91:1645-1650.
    • (2011) Signal Processing , vol.91 , pp. 1645-1650
    • Sheng, H.1    Sun, H.2    Chen, Y.3    Qiu, T.4
  • 12
    • 33745698055 scopus 로고    scopus 로고
    • Design of variable and adaptive fractional order FIR differentiators
    • Tseng C.C. Design of variable and adaptive fractional order FIR differentiators. Signal Processing 2006, 86:2554-2566.
    • (2006) Signal Processing , vol.86 , pp. 2554-2566
    • Tseng, C.C.1
  • 13
    • 84855191996 scopus 로고    scopus 로고
    • Physical experimental study of variable-order fractional integrator and differentiator
    • The 4th IFAC Workshop Fractional Differentiation and its Applications, 2010.
    • H. Sheng, H. Sun, C. Coopmans, Y.Q. Chen, G.W. Bohannan, Physical experimental study of variable-order fractional integrator and differentiator, in: Proceedings of FDA'10. The 4th IFAC Workshop Fractional Differentiation and its Applications, 2010.
    • in: Proceedings of FDA'10.
    • Sheng, H.1    Sun, H.2    Coopmans, C.3    Chen, Y.Q.4    Bohannan, G.W.5
  • 15
    • 0003896880 scopus 로고    scopus 로고
    • Fractional system identification: An approach using continuous order distributions
    • NASA/TM-1999-209640, 1999.
    • T.T. Hartley, C.F. Lorenzo, Fractional system identification: An approach using continuous order distributions, NASA/TM-1999-209640, 1999.
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 16
    • 0001342751 scopus 로고    scopus 로고
    • On the existence of the order domain and the solution of distributed order equations, part I
    • part II, 2 (2000)
    • Bagley R.L., Torvik P.J. On the existence of the order domain and the solution of distributed order equations, part I. International Journal of Applied Mathematics 2000, 2:865-882. part II, 2 (2000) pp. 965-987.
    • (2000) International Journal of Applied Mathematics , vol.2 , pp. 865-882
    • Bagley, R.L.1    Torvik, P.J.2
  • 17
    • 84855207234 scopus 로고    scopus 로고
    • Fractional and hypersingular operators in variable exponent spaces on metric measure space
    • Almeida A., Samko S. Fractional and hypersingular operators in variable exponent spaces on metric measure space. Mediterranean Journal of Mathematics 2008, 99:1-18.
    • (2008) Mediterranean Journal of Mathematics , vol.99 , pp. 1-18
    • Almeida, A.1    Samko, S.2
  • 18
    • 84855189422 scopus 로고    scopus 로고
    • On a class of fractional type integral equations in variable exponent spaces
    • Rafeiro H., Samko S. On a class of fractional type integral equations in variable exponent spaces. Fractional Calculus and Applied Analysis 2007, 10:399-421.
    • (2007) Fractional Calculus and Applied Analysis , vol.10 , pp. 399-421
    • Rafeiro, H.1    Samko, S.2
  • 19
    • 58049138945 scopus 로고    scopus 로고
    • Some new existence results for fractional differential inclusions with boundary conditions
    • Chang Y.K., Nieto J.J. Some new existence results for fractional differential inclusions with boundary conditions. Mathematical and Computer Modelling 2009, 49:605-609.
    • (2009) Mathematical and Computer Modelling , vol.49 , pp. 605-609
    • Chang, Y.K.1    Nieto, J.J.2
  • 21
    • 59149098037 scopus 로고    scopus 로고
    • Existence and approximation of solutions to fractional differential equations
    • Muslim M. Existence and approximation of solutions to fractional differential equations. Mathematical and Computer Modelling 2009, 49:1164-1172.
    • (2009) Mathematical and Computer Modelling , vol.49 , pp. 1164-1172
    • Muslim, M.1
  • 25
    • 34247154280 scopus 로고    scopus 로고
    • Global existence theory and chaos control of fractional differential equations
    • Lin W. Global existence theory and chaos control of fractional differential equations. Journal of Mathematical Analysis and Applications 2007, 332:709-726.
    • (2007) Journal of Mathematical Analysis and Applications , vol.332 , pp. 709-726
    • Lin, W.1
  • 26
    • 68349100153 scopus 로고    scopus 로고
    • Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order
    • Chang Y.K., Kavitha V., Arjunan M.M. Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order. Nonlinear Analysis TMA 2009, 71:5551-5559.
    • (2009) Nonlinear Analysis TMA , vol.71 , pp. 5551-5559
    • Chang, Y.K.1    Kavitha, V.2    Arjunan, M.M.3
  • 27
    • 71549128004 scopus 로고    scopus 로고
    • Existence and uniqueness of mild solutions to impulsive fractional differential equations
    • Mophou G.M. Existence and uniqueness of mild solutions to impulsive fractional differential equations. Nonlinear Analysis TMA 2010, 72:1604-1615.
    • (2010) Nonlinear Analysis TMA , vol.72 , pp. 1604-1615
    • Mophou, G.M.1
  • 29
    • 15544379984 scopus 로고    scopus 로고
    • Numerical simulations of fractional systems: an overview of existing methods and improvements
    • Aoun M., Malti R., Levron F., Oustaloup A. Numerical simulations of fractional systems: an overview of existing methods and improvements. Nonlinear Dynamics 2004, 38:117-131.
    • (2004) Nonlinear Dynamics , vol.38 , pp. 117-131
    • Aoun, M.1    Malti, R.2    Levron, F.3    Oustaloup, A.4
  • 30
    • 33748569516 scopus 로고    scopus 로고
    • Computation of fractional order derivative and integral via power series expansion and signal modeling
    • Ferdi Y. Computation of fractional order derivative and integral via power series expansion and signal modeling. Nonlinear Dynamics 2006, 46:1-15.
    • (2006) Nonlinear Dynamics , vol.46 , pp. 1-15
    • Ferdi, Y.1
  • 31
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • Momani S., Odibat Z. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos, Solitons & Fractals 2007, 31:1248-1255.
    • (2007) Chaos, Solitons & Fractals , vol.31 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2
  • 32
    • 33745712076 scopus 로고    scopus 로고
    • An approximate method for numerical solution of fractional differential equations
    • Kumar P., Agrawal O.P. An approximate method for numerical solution of fractional differential equations. Signal Processing 2006, 86:2602-2610.
    • (2006) Signal Processing , vol.86 , pp. 2602-2610
    • Kumar, P.1    Agrawal, O.P.2
  • 33
    • 35349007940 scopus 로고    scopus 로고
    • Numerical studies for a multi-order fractional differential equation
    • Sweilam N.H., Khader M.M., Al-Bar R.F. Numerical studies for a multi-order fractional differential equation. Physics Letters A 2007, 371:26-33.
    • (2007) Physics Letters A , vol.371 , pp. 26-33
    • Sweilam, N.H.1    Khader, M.M.2    Al-Bar, R.F.3
  • 34
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm K., Ford N.J., Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 2002, 29:3-22.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 35
    • 78049352592 scopus 로고    scopus 로고
    • Variable-order fractional derivatives and their numerical approximations
    • Valério D., Costa J.S. Variable-order fractional derivatives and their numerical approximations. Signal Processing 2011, 91:470-483.
    • (2011) Signal Processing , vol.91 , pp. 470-483
    • Valério, D.1    Costa, J.S.2
  • 36
    • 0036650827 scopus 로고    scopus 로고
    • Dynamics and control of initialized fractional-order systems
    • Hartley T., Lorenzo C.F. Dynamics and control of initialized fractional-order systems. Nonlinear Dynamics 2002, 29:201-233.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 201-233
    • Hartley, T.1    Lorenzo, C.F.2
  • 40
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • Lorenzo C.F., Hartley T.T. Variable order and distributed order fractional operators. Nonlinear Dynamics 2002, 29:57-98.
    • (2002) Nonlinear Dynamics , vol.29 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.