Uncertain Fractional Operator With Application Arising in the Steady Heat Flow

Abstract

In the recent years much efforts were made to propose simple and well-behaved fractional operators to inherit the classical properties from the first order derivative and overcome the singularity problem of the kernel appearing for the existing fractional derivatives. Therefore, we propose in this research an interesting approach to acquire the interval solution of fractional interval differential equations under a new fractional operator, that does not have the above defect with uncertain parameters. In fact, this scheme is developed to achieve the interval solution of the uncertain steady heat flow based on the fractional interval differential equations. An example is experienced to illustrate our approach and validate it.