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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 3 | Year 2016 | Article Id. IJMTT-V36P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P521

Existence of a Positive Solution for Nonlinear Differential Equations


G.U.Pawar, J.N.Salunke
Abstract

In this paper, we prove the existence result for nonlinear differential equation without using themonotonocity of upper and lower solutions.

Keywords
Fractional Differential Equation (FDE), Upper and Lower Control Functions.
References

[1] Podlubny I.,Fractional Differential Equations.Academic Press,San Diego(1999).
[2] Wang C, Wang R.,Wang S.Yang C., Positive Solution of Singular Boundary Value Problems for a Nonlinear Fractional Differential Equation, Bound.Value Probl.(2011), Art ID 297026.
[3] J.N.Nanware, Existence Result for Nonlinear initial value problems involving the Difference of two two Monotone functions. Inter. Jour. Anal. Appl., Volume 7, Number 2(2015),179-184.
[4] Zhang S. The existence of a positive solution for a fractional differential equation , J.Math.Anal.Appl. 252(2000),804-812.
[5] A.A. Kilbas, H.M.Srivastava, and J.J.Trujillo, Theory and Applications of Fractional Differential Equation , North Holland Studies. Vol.204. Elsevier(North Holland) Science Publishers,Amsterdam,2006.
[6] Delbosco D.,Rodino L.,Existence and Uniqueness for a nonlinear fractional differential equation,J.Math,Anal.Appl.204(1996),609-625.
[7] Bai Z.B., Qiu T.T. , Existence of Positive solution for a singular fractional differential equation, Appl. Math. Comput.215(2009),2761-2767.
[8] J.N.Nanware, D.B.Dhaigude, Monotone Iterative Scheme for system of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions. Math.Modelling Science Computation, Springer- Verlag,283(2012) 395-402
[9] M.M. Matar, On Existence of Positive solution for initial value problem on Nonlinear Fractional Differential Equations of order , Acta.Math.Univ.Comenianae vol.LXXXIV , 1(2015), PP 51-57.

Citation :

G.U.Pawar, J.N.Salunke, "Existence of a Positive Solution for Nonlinear Differential Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 3, pp. 137-139, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P521

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