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.
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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, 4639--4646
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):4639--4646
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): 4639--4646
Keywords
- Fractional differential equation
- positive solution
- index fixed point theorem.
MSC
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