Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima”

Quasilinearization of the Initial Value Problem for Difference Equations with "Maxima"

The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearization method is suggested to solve approximately ...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales

n this paper, at first the  concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

Monotone-iterative Technique of Lakshmikantham for the Initial Value Problem for a Differential Equation with a Step Function

A distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations

The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative  of Caputo type with order  and scale index . We es...