Qualitative and Quantitative Features of Delay Differential Equations with Biological Systems - presented by Fathalla Rihan

Qualitative and Quantitative Features of Delay Differential Equations with Biological Systems

Fathalla Rihan

Fathalla Rihan
Slide at 03:45
Types, Challenges & Qualitative Features of DDEs Some Types of DDEs (iii) Neutral Delay Differential Equations (NDDEs) take the form: /(t) = f(t,y(t),y(q(t,y(t)),y'((t,y(t) '(ß(t, where α(t, y(t)) < t, ß(t, y(t)) < t. (iv) DDEs with Ditributed Delay and Fractional Order Derivatives A general form IVP with fractional-order derivative: D⁷y(t) = = f(t,y(t),y(t -+),D¹y(t-), - ƒg(t,s,y(s))ds) Dγ = dty, dt? γ ε (0, 1]. Time-delay is incorporated to describe short-term memory of prior time, while fractional-order is included to explain long-term temporal memory. A V ⑈⑈ ⑈⑈ Fathalla Rihan (UAEU) DDEs with Glucose-Insulin Interactions NODYCON 2025 3 / 24
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Summary (AI generated)

In addition to the previously discussed types of Delay Differential Equations, we also encounter singularly perturbed Delay Differential Equations, which have numerous applications in engineering. Another variant is the delay differential equation with proportional delay, known as pantograph-type Delay Differential Equations. In this case, the time delay is proportional, presenting unique challenges in analysis and application.