EXISTENCE OF POSITIVE SOLUTIONS FOR FRACTIONAL BOUNDARY VALUE PROBLEMS

Serife Muge Ege; Fatma Serap Topaly

doi:10.11948/2017044

2017 Volume 7 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2017 > 7(2): 702-712

Next Article Previous Article

Serife Muge Ege, Fatma Serap Topaly. EXISTENCE OF POSITIVE SOLUTIONS FOR FRACTIONAL BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 702-712. doi: 10.11948/2017044

Citation:

Serife Muge Ege, Fatma Serap Topaly. EXISTENCE OF POSITIVE SOLUTIONS FOR FRACTIONAL BOUNDARY VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 702-712. doi: 10.11948/2017044

EXISTENCE OF POSITIVE SOLUTIONS FOR FRACTIONAL BOUNDARY VALUE PROBLEMS

Department of Mathematics, Ege University, Bornova, 35100 Izmir, Turkey

Abstract

Abstract

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p>1, we discuss the existence and multiplicity of positive solutions to the four point boundary value problems of nonlinear fractional differential equations. Our results extend some recent works in the literature.
- Positive solutions /
- fractional differential equations /
- fixed point theorems
MSC: 34B15;39A10

FullText(HTML)

References

[1]	B. Ahmada and G. Wang, A study of an impulsive four-point nonlocal boundary value problem of nonlinear fractional differential equations, Comput. Math. Appl., 2011, 62, 1341-1349. Google Scholar
[2]	B. Ahmad and S. Sivasundaram, On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order, Appl. Math. Comput., 2010, 217, 480-487. Google Scholar
[3]	A. Babakhani and V. D. Gejji, Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., 2003, 278, 434-442. Google Scholar
[4]	Z. B. Bai and H.S. L, Positive solutions of boundary value problems of nonlinear fractional differential equation, J. Math. Anal. Appl., 2005, 311, 495-505. Google Scholar
[5]	D. Delbosco, Fractional calculus and function spaces, J. Fract. Calc., 1994, 6, 45-53. Google Scholar
[6]	D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 1996, 204, 609-625. Google Scholar
[7]	C. Goodrich, Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett., 2010, 23, 1050-1055. Google Scholar
[8]	J. Graef and B. Yang, Positive solutions of a nonlinear fourth order boundary value problem, Commun. Appl. Nonlinear Anal., 2007, 14, 61-73. Google Scholar
[9]	D. Ji and W. Ge, Positive solution for four-point nonlocal boundary value problems of fractional order, Math. Meth. Appl. Sci., 2014, 37, 1232-1239. Google Scholar
[10]	A. A. Kilbas, H. M. Srivastava and Trujillo JJ, Theory and Applications of Fractional Differential Equations, Elsevier B.V, Netherlands, 2006. Google Scholar
[11]	M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations (A. H. Armstrong, Trans.), Pergamon, Elmsford, 1964. Google Scholar
[12]	V. Lakshmikantham and S. Leela, Theory of fractional differential inequalities and applications, Commun. Appl. Anal., 2007, 11, 395-402. Google Scholar
[13]	V. Lakshmikantham and J. Devi, Theory of fractional differential equations in a Banach space, Eur. J. Pure Appl. Math., 2008, 1, 38-45. Google Scholar
[14]	V. Lakshmikantham and S. Leela, Nagumo-type uniqueness result for fractional differential equations, Nonlinear Anal. TMA 2009, 71, 2886-2889. Google Scholar
[15]	V. Lakshmikantham, S. Leela, A Krasnoselskii-Krein-type uniqueness result for fractional differential equations, Nonlinear Anal. TMA 2009, 71, 3421-3424. Google Scholar
[16]	V. Lakshmikantham, Theory of fractional differential equations, Nonlinear Anal. TMA, 2008, 69, 3337-3343. Google Scholar
[17]	R. W. Legget and L. R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J., 1979, 28, 673-688. Google Scholar
[18]	H. Lu, Z. Han, S. Sun and J. Liu, Existence on positive solutions for boundary value problems of nonlinear fractional differential equations with p-Laplacian, Adv. Differ. Equ., 2013, 2013, 30 pp. doi:10.1186/1687-1847-2013-30 Google Scholar
[19]	R. Ma and L. Xu, Existence of positive solutions of a nonlinear fourth order boundary value problem, Appl. Math. Lett., 2010, 23, 537-543. Google Scholar
[20]	K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York. 1993,. Google Scholar
[21]	M, Rehman and R. Khan, Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations, Appl. Math. Lett., 2010, 23, 1038-1044. Google Scholar
[22]	W.Yang, Positive solution for fractional q-difference boundary value problems with -Laplacian operator, Bull. Malays. Math. Soc., 2013, 36, 1195-1203. Google Scholar
[23]	C. Yu and G. Gao, Existence of fractional differential equations, J. Math. Anal. Appl., 2005, 310, 26-29. Google Scholar
[24]	X. Zhao, C. Chai and W. Ge, Positive solutions for fractional four-point boundary value problems, Commun. Nonlinear Sci. Numer. Simul., 2011, 16, 3665-3672. Google Scholar
[25]	W. Zhou and Y. Chu, Existence of solutions for fractional differential equations with multi-point boundary conditions, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, 1142-1148. Google Scholar