使用埃尔扎基分解法与卡普托-法布里齐奥分数导数的时间分数气动力学方程的解决方法

The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...

The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, the integral equations refer to the first and second kinematic equations for velocity and position functions, respectively.
Consider an example to calculate the velocity and position from the acceleration function. A motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. Its acceleration is...

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by