Method of upper lower solutions for nonlinear system of fractional differential equations and applications
Downloads
DOI:
https://doi.org/10.26637/MJM0603/0001Abstract
Our aim is to develop the method of upper lower solutions and apply it to prove existence and uniqueness of
solution of periodic boundary value problems for a system of fractional differential equations involving a Riemann
- Liouville fractional derivatives.
Keywords:
System of fractional differential equations, Periodic boundary value problems, Riemann-Liouville fractional derivatives, Upper and lower solutions, Existence and uniqueness resultsMathematics Subject Classification:
Mathematics- Pages: 467-472
- Date Published: 01-07-2018
- Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)
R. Chaudhary and D. N. Pandey, Existence results for nonlinear fractional differential equation with nonlocal integral boundary conditions, Malaya J. Mat., 4(3)(2016), $392-403$.
D.B. Dhaigude,J.A.Nanware and V.R.Nikam,Monotone technique for weakly coupled system of Caputo fractional differential equations with periodic boundary conditions, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 19(2012),575584.
R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
N.B.Jadhav and J.A.Nanware, Integral boundary value problem for system of nonlinear fractional differential equations, Bull. Marathwada Math. Soc., 18(2)(2017), $23-31$.
A.A.Kilbas,H.M.Srivastava and J.J.Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
G.S.Ladde,V.Lakshmikantham and A.S.Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Pub.Co.Boston, 1985.
X. Liu, M. Jia and B. Wu, Existence and uniqueness of solution for fractional differential equations with integral boundary conditions, EJOTDE, $69(2009), 1-10$.
F.A.McRae, Monotone iterative technique and existence results for fractional differential Equations, Nonlinear Analysis:TMA, 71(12)(2009), 6093-6096.
Mohammed Belmekki,J.J.Nieto and Rosana RodríguezLópez,Existence of periodic solutions for a nonlinear fractional differential equation, Boundary Value Problems, $2009(2009)$ Art. ID. 324561 .
J.A.Nanware and D.B.Dhaigude, Monotone iterative scheme for system of Riemann-Liouville fractional differential equations with integral boundary conditions,Math. Modelling Science Computation, SpringerVerlag, 283(2012), 395-402.
J.A.Nanware and D.B.Dhaigude, Existence and uniqueness Of solution of Riemann-Liouville fractional differential equations with integral boundary conditions, Inter. J.Nonl. Sci., 14(4)(2012), 410-415.
J.A.Nanware,N.B.Jadhav and D.B.Dhaigude, Monotone iterative technique for finite system of Riemann-Liouville fractional differential equations with integral boundary conditions,Internat. Conf. Math. Sci., June 2014, 235238.
J.A.Nanware and D.B.Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions,J. Nonlin Sci.Appl., $7(2014), 246-254$.
J.A.Nanware and D.B. Dhaigude,Monotone technique for finite weakly coupled system of Caputo fractional differential equations with periodic boundary conditions, Dyn.Cont., Dis. Impul. Syst.Series A: Math. Anal., $22(1)(2015), 13-23$.
J.A.Nanware, N.B.Jadhav and D.B.Dhaigude, Initial value problems for fractional differential equations involving Riemann-Liouville derivative, Malaya J. Mat., 5(2)(2017), 337-345.
C.V.Pao, Nonlinear Parabolic and Elliptic Equations, New York,Plenum Press, 1992.
I. Podlubny, Fractional Differential Equations,Academic Press, San Diego, 1999.
J. Vasundhara Devi, Generalized monotone method for periodic boundary value problems of Caputo fractional differential equations, Comm. Appl.Anal., 12(4)(2008), $399-406$.
Z.Wei, W. Dong and J. Che, Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative, Nonlinear Analysis,73(2010), 3232-3238.
Similar Articles
- A. M. A. El-Sayed, Zaki. F. A. EL-Raheem, N. A. O. Buhalima, Eigenfunction expansion of the Sturm-Liouville equation with a non-local boundary condition , Malaya Journal of Matematik: Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.