|
|
 |
| |
|
|
|
On Fractional Inequalities for General Fractional Operators |
|
|
|
PP: 303-310 |
|
|
|
doi:10.18576/pfda/110206
|
|
|
|
Author(s) |
|
|
|
Mohammed Al-Refai,
|
|
|
|
Abstract |
|
|
| The Leibniz and the power law rules of differentiations do not hold for fractional derivatives with non-local kernels. Instead, infinite series representations were derived for the Leibniz and the power law rules of fractional derivatives. These rules produce heavy calculations, and they are not practical in implementations. In this paper, we derive certain inequalities of the general fractional operators of Caputo type. These inequalities are similar to the Leibniz and the power law rules for integer derivatives, where we replace the equality’s by inequalities. Because the general fractional operators involve many fractional operators as particular cases, the current study will involve several types of fractional differential and integral operators and include some recent studies in the literature as particular cases. We present several examples to illustrate the applicability of the obtained results.
|
|
|
|
|
|
|
|
