Existence Result for Nonlinear Initial Value Problems Involving the Difference of Two Monotone Functions

Main Article Content

J.A. Nanware

Abstract

In this paper, monotone iterative technique for nonlinear initial value prob-lems involving the difference of two functions is developed. As an application ofthis technique, existence of solution of nonlinear initial value problems involvingthe difference of two functions is obtained.

Article Details

References

  1. T.G.Bhaskar, F.A.McRae, Monotone Iterative Techniques for Nonlinear Problems Involving The Difference of Two Monotone Functions, Applied Mathematics and Computation 133 (2002), 187-192.
  2. J.Vasundhara Devi, F.A.McRae, Z. Drici, Variational Lyapunov Method for Fractional Differential Equations, Computers and Mathematics with Applications,64 (2012), 2982-2989.
  3. D.B.Dhaigude, J.A.Nanware and V.R.Nikam, Monotone Technique for System of Caputo Fractional Differential Equations with Periodic Boundary Conditions, Dynamics of Continuous, Discrete and Impulsive Systems, 19 (2012), 575-584.
  4. A.A. Kilbas, H.M.Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North Holland Mathematical Studies Vol.204. Elsevier(North-Holland) Sciences Publishers, Amsterdam, 2006.
  5. G.S.Ladde, V.Lakshmikantham, A.S.Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Advanced Publishing Program, London, 1985.
  6. V.Lakshmikantham, A.S.Vatsala, Theory of Fractional Differential Equations and Applications, Communications in Applied Analysis 11 (2007), 395-402.
  7. V.Lakshmikantham, A.S.Vatsala, Basic Theory of Fractional Differential Equations and Applications, Nonlinear Analysis, 69 (2008), 2677-2682.
  8. V.Lakshmikantham, A.S.Vatsala, General Uniqueness and Monotone Iterative Technique for Fractional Differential Equations, Applied Mathematics Letters, 21 (2008), no.8, 828-834.
  9. V. Lakshmikantham, S. Leela and J.V. Devi, Theory and Applications of Fractional Dynamical Systems, Cambridge Scientific Publishers Ltd., 2009.
  10. B.Mandelbrot, The Fractional Geometry of Nature, Freeman, San Francisco, 1982.
  11. F.A.McRae, Monotone Iterative Technique and Existence Results for Fractional Differential Equations, Nonlinear Analysis, 71 (2009), no.12, 6093-6096.
  12. J.A.Nanware, Existence and Uniqueness of solution of Fractional Differential Equations Via Monotone Method, Bull. Marathwada Maths. Society, 14 (2013), 39-55.
  13. J.A.Nanware, Monotone Method In Fractional Differential Equations and Applications, Dr.Babsaheb Ambedkar Marathwada University, Ph.D Thesis, 2013.
  14. J.A.Nanware, G.A.Birajdar, Methods of Solving Fractional Differential Equations of Order α(0 < α < 1), Bull. Marathwada Maths. Society, 15 (2014), 40-53.
  15. J.A.Nanware, D.B.Dhaigude, Existence and Uniqueness of solution of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions, Int. Jour. Nonlinear Science, 14 (2012), 410-415.
  16. J.A.Nanware, D.B.Dhaigude, Monotone Iterative Scheme for System of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions, Math.Modelling Scien.Computation, Springer-Verlag, 283 (2012), 395-402.
  17. J.A.Nanware, D.B.Dhaigude, Existence and Uniqueness of Solution of Differential Equations of Fractional Order with Integral Boundary Conditions, J. Nonlinear. Sci. Appl., 7 (2014), 246-254.
  18. J.A.Nanware, D.B.Dhaigude, Boundary Value Problems for Differential Equations of Noninteger Order Involving Caputo Fractional Derivative, Adv. Stu. Contem. Math., 24 (2014), 369-376.
  19. J.A.Nanware, D.B.Dhaigude, Monotone Technique for Finite System of Caputo Fractional Differential Equations with Periodic Boundary Conditions, Dynamics of Continuous, Discrete and Impulsive Systems. (Accepted)
  20. J.A.Nanware, N.B.Jadhav, D.B.Dhaigude, Monotone Iterative Technique for Finite System of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions, International Conference of Mathematical Sciences 2014, Elsevier, 235-238 (2014).
  21. I.Podlubny, Fractional Differential Equations, San Diego, Academic Press, 1999.