Initial value problems for fractional differential equations involving Riemann-Liouville derivative

J.A. Nanware a∗ , N.B. Jadhav b and D.B. Dhaigude c

Initial value problems for fractional differential equations involving Riemann-Liouville derivative

Authors :

J.A. Nanware^a∗ , N.B. Jadhav^b and D.B. Dhaigude ^c

Author Address :

^a Department of Mathematics, Shrikrishna Mahavidyalaya, Gunjoti–413 606, Maharashtra, India.
^b Department of Mathematics, Yashwantrao Chavan Mahavidyalaya, Tuljapur– 413 605, India.
^cDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004, Maharashtra, India.

*Corresponding author.

Abstract :

Existence results are obtained for fractional differential equations with $C_{p}$ continuity of functions. Monotone method for nonlinear initial value problem is developed by introducing the notion of coupled lower and upper solutions. As an application of the method existence and uniqueness results are obtained.

Keywords :

Fractional derivative, initial value problem, coupled lower and upper solutions, existence and uniqueness.

DOI :

Article Info :

Received : December 07, 2016; Accepted : December 23, 2016.