J. Vasundhara Devi

The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments

In this paper, we initiate the study of the method of upper and lower solutions and monotone iterative technique for impulsive differential equations with variable moments. Because of the difficult nature of the problem, we shall restrict ourselves to a simple situation which, as we shall see, presents enough complications.

Stability criteria for set differential equations

Notions of stability for the solutions of set differential equations, using Lyapunov-like functions are considered. Criteria for the equistability, equiasymptotic stability, uniform and uniform asymptotic stability are presented.

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.

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.

Set differential systems and vector lyapunov functions

We prove a comparison result in terms of vector Lyapunov-like functions relative to a set differential system. Using this, we provide sufficient conditions in terms of vector Lyapunov-like functions for the stability properties of the trivial solutions of set differential systems.

Nonuniform stability and boundedness criteria for set differential equations

Notions of nonuniform stability and boundedness criteria for the solutions of Set Differential Equations (SDEs), using Lyapunov-like functions, under less restrictive assumptions are studied in this article.

Can Fractional Calculus be Generalized: Problems and Efforts

Fractional order calculus always includes integer-order too. The question that crops up is: Can it be a widely accepted generalized version of classical calculus? We attempt to highlight the current problems that come in the way to define the fractional calculus that will be universally accepted as a perfect generalized version of integer-order calculus and to point out the efforts in this direction. Also, we discuss the question: Given a non-integer fractional order differential equation as a mathematical model can we readily write the corresponding physical model and vice versa in the same way as we traditionally do for classical differential equations? We demonstrate numerically computationally the pros and cons while addressing the questions keeping in the background the generalization of the inverse of a matrix.