Existence and multiplicity of solutions for nonlinear fractional differential equations

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Authors
Hamidreza Marasi
 Department of Mathematical sciences, Basic Science Faculty, Bonab University, Bonab, Iran.
Hossein Piri
 Department of Mathematical sciences, Basic Science Faculty, Bonab University, Bonab, Iran.
Hassen Aydi
 Department of Mathematics, College of Education of Jubail, University of Dammam, P. O: 12020, Industrial Jubail 31961, Saudi Arabia.
 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
Abstract
In this paper, we consider the following fractional initial value problems:
\[D^\alpha u(t) = f(t; u(t);D^\beta u(t)); t \in (0; 1];\]
\[u^{(k)}(0) = \eta_k; k = 0; 1; ...; n  1;\]
where \(n  1 < \beta < \alpha < n; (n \in N)\) are real numbers, \(D^\alpha\) and \(D^\beta\) are the Caputo fractional derivatives and
\(f \in C([0; 1] \times R)\). Using the fixed point index theory, we study the existence and multiplicity of positive
solutions and obtain some new results.
Share and Cite
ISRP Style
Hamidreza Marasi, Hossein Piri, Hassen Aydi, Existence and multiplicity of solutions for nonlinear fractional differential equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 46394646
AMA Style
Marasi Hamidreza, Piri Hossein, Aydi Hassen, Existence and multiplicity of solutions for nonlinear fractional differential equations. J. Nonlinear Sci. Appl. (2016); 9(6):46394646
Chicago/Turabian Style
Marasi, Hamidreza, Piri, Hossein, Aydi, Hassen. "Existence and multiplicity of solutions for nonlinear fractional differential equations." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 46394646
Keywords
 Fractional differential equation
 positive solution
 index fixed point theorem.
MSC
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