Existence of Solutions for Fractional Differential Equation with Nonlocal Boundary Condition
- 1Department of Mathematics, Karpagam University, Coimbatore, India
- 2Research Department of Mathematics, H.H. The Rajah’s College, Pudukkottai - 622 001, India
Res. J. Recent Sci., Volume 5, Issue (9), Pages 45-50, September,2 (2016)
By using standard Riemann-Liouville differentiation and Leray- Shauder theory, existence of non negative solutions for fractional differential equation with global boundary condition +s( ) g( ,v( )) =0, 0< <0.99, v(0)=0, v(0.99)= is considered, here b (1,2] is a real number, the standard Riemann-Liouville differentiation is , and
- A.M.A. El-Sayed (1998)., Nonlinear functional-differential equations of arbitrary orders., Nonliner Analysis: Theory, Methods & Applications, 33(2), 181-186.
- Kilbas A.A., Samko S.G., and Marchery O. I. (1993)., Fractional Integrals and Derivatives., Gordon and Breach Science Publishers, Yverdon, Switzerland.
- Kilbas A.A. and Trujillo J.J. (2002)., Differential equations of fractional order: methods, results and problems. II., Applicable Analysis, 81, (2), 435-493.
- Kilbas A.A. and Trujillo J.J. (2001)., Differential equations of fractional order: methods results and problems. I., Applicable Analysis., 78(1-2), 153-192.
- Miller K.S. and Ross B. (1993)., An Introduction to the Fractional Calculus and Fractional Differential Equations., John Wiley & Sons, New York, NY, USA.
- Podlubny I. (1999)., Fractional Differential Equations., 198, Academic Presas, San Diego, Calif, USA.
- Miller K.S. (1993)., Fractional differential equations., Journal of Fractional Calculus, 3, 49-57.
- Podlubny I. (1994)., The Laplace transform method for liner differential equations of the fractional order., UEF02-94, Institute of Expermental Physics, Slovak Academy of Sciences, Kosice, Solvakia.
- Babakhani A. and Daftardar Gejii V. (2003)., Existence of positive solutions of nonlinear fractional differential equations., Journal of Mathematical Analysis and Applications, 278(2), 432-442.
- Delbosco D. (1994)., Fractional calculus and function spaces., Journal of Fractional Calcululs, 6, 45-53.
- Delbosco D. and Rodino L. (1996)., Existence and uniqueness for a nonlinear fractional differential equation., Journal of Mathematical Analysis and Applications, 204(2), 609-625.
- Daftan Gejji V. and Babakhari A. (2004)., Analysis of a system of fractional differential equation., Journal of Mathematical Analysis and Applications, 293(2), 511-522.
- Zhang S.Q. (2000)., The Existence of positive solution for a nonlinear fractional differential equation., Journal of Mathematical Analysis and Applications, 252, (2), 804-812.
- Zhang S. Q. (2003)., Existence of positive solution for some class of nonlinear fractional differential equation., Journal of Mathematical Analysis and Applications, 278(1), 136-148.
- Bai Z.B. and Lu H. (2005)., Positive solutions for boundary value problem of nonlinear fractional differentrial equations., Journal of Mathematical Analysis and Applications, 311(2), 495-505.
- Bai Z. B. (2010)., On Positive solutions of a nonlocal fractional boundary value problem, differential., Nonlinar Analysis Theory, Methods & Application, 72(2), 916-924.
- Wang Y.Q., Liu L.s., and Wu Y.H. (2011)., Positive solutions for a nonlocal fractional differential equation., Nonlinear Analysis Thoery, Methods & Applications, 74(11), 3599-3605.
- Krasnoselskii M.A. (1984)., Positive Solutions of Operator Equations., P. Noordhoff Ltd., Groninen, The Netherelands.
- Leggett R.W. and Williams L.R. (1979)., Multiple positive fixed points of nonlinear operators on ordered Banach spaces., Indian University Mathematical Journal, 28(4), 673-688.
- Gao Hongliang and Han Xiaoling (2011)., Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition., International Journal of Differential Equations, 2011, 10.