Bibliographic Details
| Title: |
Bounds, Decay, and Integrals of Non-Increasing Functions: A Comprehensive Analysis. |
| Authors: |
Tarek, Bahloul1 bahloul.tarek@univguelma.dz |
| Source: |
IAENG International Journal of Applied Mathematics. Aug2024, Vol. 54 Issue 8, p1581-1585. 5p. |
| Subject Terms: |
*INTEGRAL functions, *WAVE equation, *DIFFERENTIAL equations, *DYNAMICAL systems, *VISCOELASTICITY |
| Abstract: |
This scientific article investigates non-increasing functions and their integral properties, shedding light on their behavior. By examining ∫∞ 0 h(s)ds = 1 − l > 0. Furthermore, examining h(t) = ∫ ∞ t E α+1(s)ds about E(t) and T > 0, we establish ∫ ∞ t E α+1(s)ds ≤ T Eα (0)E(t), showing how E(t) influences h(t). For t ≥ T, E α+1(t) follows a power-law decay. Our study unveils a set of inequalities providing insights into these relationships, offering potential applications in control theory, differential equations, and dynamical systems. [ABSTRACT FROM AUTHOR] |
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| Database: |
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