Asymptotic Properties of Neutral Differential Equations with Variable Coefficients

Linear fractional differential equations with variable coefficients

This work is devoted to the study of solutions around an α-singular point x0 ∈ [a, b] for linear fractional differential equations of the form [Lnα(y)](x) = g(x, α), where [Lnα(y)](x) = y(nα)(x)+ n−1 ∑ k=0 ak(x)y (kα)(x) with α ∈ (0, 1]. Here n ∈ N , the real functions g(x) and ak(x) (k = 0, 1, . . . , n−1) are defined on the interval [a, b], and y(nα)(x) represents sequential fractional deriva...

Asymptotic behavior of impulsive neutral delay differential equations with positive and negative coefficients of Euler form

An Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

Oscillation Properties of a Class of Neutral Differential Equations with Positive and Negative Coefficients

In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear neutral delay differential equations of the form (E) d dt (r(t) d dt (y(t) + p(t)y(t− τ))) + f1(t)G1(y(t− σ1))− f2(t)G2(y(t− σ2)) = g(t) and d dt (r(t) d dt (y(t) + p(t)y(t− τ))) + f1(t)G1(y(t− σ1))− f2(t)G2(y(t− σ2)) = 0 are studied under the assumptions ∞ ∫ 0 dt r(t) <∞ and ∞ ∫