Existence of Periodic Solution for a Nonlinear Fractional Differential Equation
By Mohammed Belmekki, J. J. Nieto, Rosana Rodríguez-López. 2009
176 citations recorded by the source corpus.
We study the existence of solutions for a class of fractional differential equations. Due to the singularity of the possible solutions, we introduce a new and proper concept of periodic boundary value conditions. We present Green's function and give some existence results for the linear case and then we study the nonlinear problem.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/3fe3e085272752a5b2218a5d636b25184105ae2d
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In Applied Mathematics
- Bashir Ahmad
- J. J. Nieto
- Juan Trujillo
- Asadollah Aghajani
- Rosana Rodríguez-López
- Ehsan Pourhadi
- Seenith Sivasundaram
- Saudi Arabia
In Modeling and Simulation
- Bashir Ahmad
- J. J. Nieto
- Juan Trujillo
- Asadollah Aghajani
- Ehsan Pourhadi
- Seenith Sivasundaram
- Saudi Arabia
- Eva Kaslik
In Numerical Analysis
- Bashir Ahmad
- J. J. Nieto
- Asadollah Aghajani
- Ehsan Pourhadi
- Rosana Rodríguez-López
- Juan Trujillo
- Saudi Arabia
- Stepan A. Tersian
Citations in the corpus
- Multiple solutions to boundary value problem for impulsive fractional differential equations (2014, background): “[1], Chen and Tang [6], and Bonanno et al.”
- RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL BOUNDARY CONDITIONS (2012, background): “Some recent work on boundary value problems of fractional order can be found in [1, 2, 3, 4, 5, 6, 7, 8, 10, 16] and the references therein.”
- Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces (2013, methodology): “[31] studied the solvability for a coupled system of nonlinear fractional differential equations in a Banach space using the measures of noncompactness and the well-known fixed point theorem of Mönch type (see also [4], [5], [9], [11], [16], [27]-[29], [37]).”
- Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆ (2011, background): “Moreover, several results concerning the existence of solutions of periodic boundary problems for fractional differential equations have been recently reported in [5, 7, 28, 37].”