F.A. McRae

Generalized quasilinearization for fractional differential equations

Abstract In this paper, an existence and uniqueness result is obtained for an IVP of fractional differential equations using the method of generalized quasilinearization, which allows for some relaxation on the conditions on f .

Set differential equations with causal operators

We obtain some basic results on existence, uniqueness, and continuous dependence of solutions with respect to initial values for set differential equations with causal operators.

Perturbing Lyapunov functions and stability criteria for initial time difference

Stability criteria for differential equations where the initial time for each solution is different is developed using the method of perturbing Lyapunov functions.

Impulsive set differential equations with delay

The basic theory of set impulsive set differential equations with delay is initiated by combining the theories of impulsive differential equations, set differential equations in metric spaces and delay differential equations.

Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions

We prove a fundamental theorem concerning the existence of coupled maximal and minimal solutions of the dynamical systems involving the difference of two monotone functions. Besides the relevance of such problems in mathematical biology, this treatment has several implications to the theory of monotone iterative techniques, as has been pointed in the several remarks made in the paper.

Miscellaneous Topics in Causal Systems

This chapter deals with extensions and generalizations of causal differential equations to other important areas of nonlinear analysis. We begin with the set differential equations with causal operators naming them as causal set differential equations (CSDE). Set differential equations in a metric space has gained much attention recently due to its applicability to multivalued differential inclusions and fuzzy differential equations and its inclusion of ordinary differential systems as a special case. The generalization of this dynamic system to include causal differential equations would cover a wider variety of situations and therefore, it would initiate an interesting and useful branch of nonlinear analysis that requires further investigation.