Monotone iterative method for a class of nonlinear fractional differential equations

Fractional Calculus and Applied Analysis

Volumn 15, Issue 2, 2012, Pages 244-252

  Wang, Guotao ^a   Baleanu, Dumitru ^b,c   Zhang, Lihong ^a  

^a SHANXI NORMAL UNIVERSITY   (China)

^b CANKAYA UNIVERSITY   (Turkey)

^c INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

Comparison theorem; Extremal solutions; Monotone iterative technique; Nonlinear fractional differential equation

Indexed keywords

EID: 84866054434     PISSN: 13110454     EISSN: 13142444     Source Type: Journal    
DOI: 10.2478/s13540-012-0018-z     Document Type: Article

References (14)

1. A. Aghajani, Y. Jalilian, J.J. Trujillo, On the existence of solutions of fractional integro-differential equations. Fract. Calc. Appl. Anal. 15, No 1 (2012), 44-69; DOI: 10.2478/s13540-012-0005-4; at http://www.springerlink.com/ content/1311-0454/15/1/
2. D. Baleanu, T. Avkar, Lagrangians with linear velocities within Riemann-Liouville fractional derivatives. Nuovo Cimento B. 119 (2004), 73-79.
3. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods (Series on Complexity, Nonlinearity and Chaos). World Scientific (2012); http://www.worldscibooks.com/mathematics/8180.html
4. D. Baleanu, O.G. Mustafa, R.P. Agarwal, On Lp-solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 218 (2011), 2074-2081.
5. S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R.L. Magin, Transient chaos in fractional Bloch equations. Comput. Math. Appl., To appear (2012); http://dx.doi.org/10.1016/j.camwa.2012.01.069
6. K. Diethelm, N.J. Ford, A.D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29 (2002), 3-22.
7. R. Hilfer (Editor), Applications of Fractional Calculus in Physics. World Scientific Pub. Co, Singapore (2000).
8. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, (2006).
9. V. Kiryakova, Generalized Fractional Calculus and Applications. Pitman Research Notes in Mathematics, Vol. 301. Longman & J. Wiley, Harlow & N. York (1994).
10. G.S. Ladde, V. Lakshmikantham, A.S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman Pub. Co., Boston (1985).
11. R.L. Magin, Fractional Calculus in Bioengineering. Begell House Publisher, Inc. Connecticut, (2006).
12. I. Podlubny, Fractional Differential Equations. Academic Press, San Diego, CA (1999).
13. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Switzerland (1993).
14. J.A. Tenreiro-Machado, Discrete-time fractional-order controllers. Fract. Calc. Appl. Anal. 4, No 1 (2001), 47-68; http://www.math.bas.bg/fcaa