On A Class of Fractional Differential Equations with Arbitrary Singularities

Abstract

In this paper, we consider a class of singular fractional differential equations such that its right hand side has an arbitrary singularity on certain interval of the real axis. We obtain new results on the existence and uniqueness of solutions using some classical fixed point theorems.                                                                                                                                                                                                                                                                                                                                                                                                                        

      

Keywords

• caputo derivative
• differential equations
• existence
• fixed point
• singularity
• uniqueness

References

1. [1] Z. Dahmani, M.Z. Sarikaya: A Generalized Lane-Emden Fractional Differential System And Its D-Stability, JARDCS Journal of IASR, Accepted 2015.
2. [2] Z. Dahmani, L. Tabharit: Fractional Order Differential Equations Involving Caputo Derivative, Theory And Applications Of Mathematics & Computer Science., 4 (1), (2014), pp. 40–55.
3. [3] Z. Dahmani, L. Tabharit: Solvability For A BVP With Caputo Derivative, J.I.M. of Taru, Accepted, 2014.
4. [4] Z. Dahmani, A.Taieb: A Coupled System Of Nonlinear Differential Equations Involing m Nonlinear Terms, Georgian Mathematical Journal., 2015.
5. [5] Z. Dahmani, A. Taieb: Solvability Of A Coupled System Of Fractional Differential Equations With Periodic And Antiperiodic Boundary Conditions, Pure And Applied Math Letters., 2015.
6. [6] Z. Dahmani, A. Taieb: New Existence And Uniqueness Results For High Dimensional Fractional Differential Systems, Ser. Math. Inform., 2015.
7. [7] M. Houas, Z. Dahmani: Coupled Systems Of Integro-Differential Equations Involving Riemann-Liouville Integrals And Caputo derivatives, Acta Univ. Appulensis., 2014.
8. [8] M. Houas, Z. Dahmani: New Results For A System Of Two Fractional Differential Equations Involving n Caputo Derivatives, Krag. J.Math., 2014. pp. 30-42.

9. [9] W.H. Jiang: Solvability For A Coupled System Of Fractional Differential Equations At Resonance, Nonlinear Anal. Real World Appl., 13, (2012), pp. 2285-2292.
10. [10] A.A. Kilbas, S.A. Marzan: Nonlinear Differential Equation With The Caputo Fraction Derivative In The Space Of Continuously Differentiable Functions, Differ. Equ., 41(1), (2005), pp. 84-89.
11. [11] Lakshmikantham, A.S. Vatsala: Basic Theory Of Fractional Defferential Equations, Nonlinear Anal., (2008), pp. 2677-2682.
12. [12] M. Li, Y. Liu: Existence And Uniqueness Of Positive Solutions For A Coupled System Of Nonlinear Fractional Differential Equations, Open Journal Of Applied Sciences., 3, (2013), pp. 53-61.
13. [13] S.M. Mechee, N. Senu: Numerical Studies Of Fractional Differential Equations Of Lane-Emden Type By Method Of Collocation, Applied Mathematics., 3, (2012), pp. 851-856.
14. [14] L. Podlubny: Fractional Differential Equations, Academic Press, New York, (1999).