In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for n−th order delay differential equation (E) ` r(t) ˆ x ′(t) ̃ γ ́(n−1) + q(t)xγ(τ (t)) = 0. The presented technique essentially simplifies the examination...

Fractional integro-differential equations arise in the mathematical modelling of various physical phenomena like heat conduction in materials with memory, diffusion processes etc. In this paper, we have taken the fractional integro-differential equation of type Dy(t) = a(t)y(t) + f(t) + ∫ t

Abstract The functional equations, functional integral equations and functional differential equations have many applications in nonlinear analysis. Also, the fractional order integral equations and fractional order differential equations have many applications in mathematical physics. Here we study the existence of solutions of a functional integral equations of arbitrary (fractional) order in...

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

Abstract. In this study we developed and modified Taylor expansion method for approximating the solution of linear Fredholm and Volterra integro-differential equations. Via Taylor’s expansion of the unknown function at an arbitrary point, the integro-differential equations to be solved is approximately transformed into a system of linear equations for the unknown and its derivatives which can b...

This paper proposes a new technique to solve n-th order linear uncertain but bounded (interval) differential equations with interval initial conditions using the interval midpoint. First, the interval differential equation is solved in terms of the interval midpoint. This solution is then used to find the solution of the original interval differential equation. The method is discussed by consid...

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We pre...

This paper is about the design of a Sliding Mode Controller (SMC), with modified PI-D sliding surface, for the control of First Order Plus Dead Time (FOPDT) process. In the modified PI-D sliding surface, error is connected to the proportional and integral elements of the controller, and the derivative of the system output is connected to derivative element of the controller. The usage of PI-D s...

In (Kolev et al., 2002) the authors proposed and analyzed a model of the competition between single cell cancer and cell-mediated immunity. The model is a bilinear system of integro-differential equations. This model was modified and generalized in (Kolev, 2002a) in order to consider the role of Th cells and antigen-presenting cells (APCs) in cellular immunity. The simulations in (Kolev, 2002a)...