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Abstract: This study explores fractional differential equations using fractional calculus techniques, extending the traditional Frobenius method with approaches like the ZZ transform and binomial ...
Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...
Department of Chemical Engineering, Loughborough University, Leicestershire, LE11 3TU, U.K., and Faculty of Chemical & Natural Resources Engineering, Universiti Malaysia Pahang, Lebuhraya Tun Razak, ...
The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other ...
1 Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia 2 Department of Mathematics, Jimma University, Jimma, Ethiopia A uniformly convergent numerical scheme is ...
Heat energy plays an essential role in numerous engineering applications, from thermal management in electronic devices to the design of efficient energy systems. Understanding and predicting the ...
When an object is given an initial velocity and is affected by gravitational acceleration and air resistance, it follows a specific path known as projectile motion. Athletes often perform this type of ...
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