Our attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power ...

A class of tempered fractional differential equations with terminal value problems are investigated in this paper. Discretized collocation methods on piecewise polynomials spaces are proposed for solving these equations. ...

In this paper, systems of fuzzy fractional differential equations with a lateral type of the Hukuhara derivative and the generalized Hukuhara derivative are numerically studied. Collocation method on discontinuous piecewise ...

We develop and analyze a new mathematical model for intravenous drug administration and the associated diffusion process. We use interval analysis to obtain a system of weakly singular Volterra integral equations over ...

A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept ...

Terminal value problems of fractional nonlinear systems are studied in this paper. The existence and uniqueness are given. The regularity of the solution is obtained in the weighted spaces. Discretized piecewise polynomial ...