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Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT 

Year 2011, Volume: 40 Issue: 2, 331 - 340, 01.02.2011

References

  • Deekshitulu, Gvsr. Generalized monotone iterative technique for fractional R-L differential equations, Nonlinear Studies 16 (1), Pages 85–94, 2009.
  • Hu, T. C., Qian, D. L. and Li C. P. Comparison theorems of fractional differential equations, Comm. Appl. Math. Comput. 23 (1), 97–103, 2009.
  • K¨oksal, S. and Yakar, C. Generalized quasilinearization method with initial time difference, Simulation, an International Journal of Electrical, Electronic and other Physical Systems 24(5), 2002.
  • Ladde, G. S, Lakshmikantham, V. and Vatsala A. S. Monotone Iterative Technique for Non- linear Differential Equations(Pitman Publishing Inc., Boston, 1985).
  • Lakshmikantham, V., Leela, S. and Vasundhara, Devi J. Theory of Fractional Dynamic Systems(Cambridge Academic Publishers, Cambridge, 2009).
  • Lakshmikantham, V. and Vatsala, A. S. General uniqueness and monotone iterative tech- nique for fractional differential equations, Applied Mathematics Letters 21 (8), 828–834, 2008. [7] Lakshmikantham, V. and Vatsala, A. S. Basic theory of fractional differential equations, Nonlinear Analysis: Theory, Methods and Applications 69 (8), 2677–2682, 2008.
  • McRae, F. A. Monotone iterative technique and existence results for fractional differential Equations, Nonlinear Analysis: Theory, Methods and Applications 71 (12), 6093–6096, 2009. [9] McRae, F. A. Monotone iterative technique for PBVP of Caputo fractional differential equa- tions, to appear.
  • Oldham, K. B. and Spanier, J. The Fractional Calculus (Academic Press, New York, 1974). [11] Podlubny, I. Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applica- tions(Mathematics in Science and Engineering, 198, Academic Press, San Diego, 1999).
  • Vasundhara Devi, J. Generalized monotone technique for periodic boundary value problems of fractional differential equations, Communications in Applied Analysis 12 (4), 399–406, 2008. [13] Yakar, C. and Yakar, A. An extension of the quasilinearization method with initial time dif- ference, Dynamics of Continuous, Discrete and Impulsive Systems (Series A: Mathematical Analysis) DCDIS 14 (S2) 1-305, 275–279, 2007.
  • Yakar, C. and Yakar, A. Further generalization of quasilinearization method with initial time differenceJ. of Appl. Funct. Anal. 4 (4), 714–727, 2009.
  • Yakar, C. and Yakar. A. A refinement of quasilinearization method for Caputo sense frac- tional order differential equations, Abstract and Applied Analysis 2010, Article ID 704367, 10 pages, doi:10.1155/2010/704367

Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT 

Year 2011, Volume: 40 Issue: 2, 331 - 340, 01.02.2011

References

  • Deekshitulu, Gvsr. Generalized monotone iterative technique for fractional R-L differential equations, Nonlinear Studies 16 (1), Pages 85–94, 2009.
  • Hu, T. C., Qian, D. L. and Li C. P. Comparison theorems of fractional differential equations, Comm. Appl. Math. Comput. 23 (1), 97–103, 2009.
  • K¨oksal, S. and Yakar, C. Generalized quasilinearization method with initial time difference, Simulation, an International Journal of Electrical, Electronic and other Physical Systems 24(5), 2002.
  • Ladde, G. S, Lakshmikantham, V. and Vatsala A. S. Monotone Iterative Technique for Non- linear Differential Equations(Pitman Publishing Inc., Boston, 1985).
  • Lakshmikantham, V., Leela, S. and Vasundhara, Devi J. Theory of Fractional Dynamic Systems(Cambridge Academic Publishers, Cambridge, 2009).
  • Lakshmikantham, V. and Vatsala, A. S. General uniqueness and monotone iterative tech- nique for fractional differential equations, Applied Mathematics Letters 21 (8), 828–834, 2008. [7] Lakshmikantham, V. and Vatsala, A. S. Basic theory of fractional differential equations, Nonlinear Analysis: Theory, Methods and Applications 69 (8), 2677–2682, 2008.
  • McRae, F. A. Monotone iterative technique and existence results for fractional differential Equations, Nonlinear Analysis: Theory, Methods and Applications 71 (12), 6093–6096, 2009. [9] McRae, F. A. Monotone iterative technique for PBVP of Caputo fractional differential equa- tions, to appear.
  • Oldham, K. B. and Spanier, J. The Fractional Calculus (Academic Press, New York, 1974). [11] Podlubny, I. Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applica- tions(Mathematics in Science and Engineering, 198, Academic Press, San Diego, 1999).
  • Vasundhara Devi, J. Generalized monotone technique for periodic boundary value problems of fractional differential equations, Communications in Applied Analysis 12 (4), 399–406, 2008. [13] Yakar, C. and Yakar, A. An extension of the quasilinearization method with initial time dif- ference, Dynamics of Continuous, Discrete and Impulsive Systems (Series A: Mathematical Analysis) DCDIS 14 (S2) 1-305, 275–279, 2007.
  • Yakar, C. and Yakar, A. Further generalization of quasilinearization method with initial time differenceJ. of Appl. Funct. Anal. 4 (4), 714–727, 2009.
  • Yakar, C. and Yakar. A. A refinement of quasilinearization method for Caputo sense frac- tional order differential equations, Abstract and Applied Analysis 2010, Article ID 704367, 10 pages, doi:10.1155/2010/704367
There are 11 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Coşkun Yakar This is me

 ali Yakar

Publication Date February 1, 2011
Published in Issue Year 2011 Volume: 40 Issue: 2

Cite

APA Yakar, C., & Yakar, . (2011). Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics, 40(2), 331-340.
AMA Yakar C, Yakar . Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. February 2011;40(2):331-340.
Chicago Yakar, Coşkun, and  ali Yakar. “Monotone Iterative Technique With Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 40, no. 2 (February 2011): 331-40.
EndNote Yakar C, Yakar  (February 1, 2011) Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics 40 2 331–340.
IEEE C. Yakar and  . Yakar, “Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT ”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, pp. 331–340, 2011.
ISNAD Yakar, Coşkun - Yakar, ali. “Monotone Iterative Technique With Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics 40/2 (February 2011), 331-340.
JAMA Yakar C, Yakar . Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2011;40:331–340.
MLA Yakar, Coşkun and  ali Yakar. “Monotone Iterative Technique With Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT ”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, 2011, pp. 331-40.
Vancouver Yakar C, Yakar . Monotone Iterative Technique with Initial Time Difference for Fractional Differential Equations  ABSTRACT  |  FULL TEXT . Hacettepe Journal of Mathematics and Statistics. 2011;40(2):331-40.