Consider the first-order linear delay differential equation x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, and the second-order linear delay equation x′′(t) + p(t)x(τ(t)) = 0, t ≥ t0, where p and τ are continuous functions on [t0,∞), p(t) > 0, τ(t) is nondecreasing, τ(t) ≤ t for t ≥ t0 and limt→∞ τ(t) = ∞. Several oscillation criteria are presented for the first-order equation when

In this paper, a numerical method named as Initial Value Technique (IVT) is suggested to solve singularly perturbed boundary value problems for second order ordinary differential equations of reactiondiffusion type with a delay (negative shift). In this technique, the original problem of solving the second order differential equation is reduced to solving four first order singularly perturbed d...

This study establishes the existence and stability of solutions for a general class Riemann–Liouville (RL) fractional differential equations (FDEs) with variable order finite delay. Our findings are confirmed by fixed-point theorems (FPTs) from available literature. We transform RL FDE to alternate integral structure, then use classical FPTs, results studied Hyers–Ulam is established help stand...

Wavelet transforms or wavelet analysis represent a recently created mathematical tool for assistance in resolving various issues. Wavelets can also be used numerical analysis. In this study, we solve pantograph delay differential equations using the Modified Laguerre method (MLWM), an effective technique. Fractional derivatives are defined Caputo operator. The convergence of suggested strategy ...