TY  - JOUR
ID  - Denton2017
LB  - Denton2017
AU  - Denton, Z.
AU  - Ramírez, J. D.
TI  - Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems
ST  - Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 5
SP  - 705
EP  - 724
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.5.705
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.5.705
AB  - In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
KW  - Riemann Liouville derivative
KW  - integro-differential equation
KW  - monotone method
SN  - 1232-9274
ER  -