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An algorithm for the numerical solution of differential equationsof fractional order
Zaid M. Odibat,Shaher Momani 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.1
We present and discuss an algorithm for the numerical solution of initial value problems of the form D y(t) = f(t, y(t)), y(0) = y0, where D y is the derivative of y of order in the sense of Caputo and 0 < 1. The algorithm is based on the fractional Euler’s method which can be seen as a generalization of the classical Euler’s method. Numerical examples are given and the results show that the present algorithm is very effective and convenient. We present and discuss an algorithm for the numerical solution of initial value problems of the form D y(t) = f(t, y(t)), y(0) = y0, where D y is the derivative of y of order in the sense of Caputo and 0 < 1. The algorithm is based on the fractional Euler’s method which can be seen as a generalization of the classical Euler’s method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.
AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
Odibat, Zaid M.,Momani, Shaher Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.1
We present and discuss an algorithm for the numerical solution of initial value problems of the form $D_*^\alpha$y(t) = f(t, y(t)), y(0) = y0, where $D_*^\alpha$y is the derivative of y of order $\alpha$ in the sense of Caputo and 0<${\alpha}{\leq}1$. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.
DC Motor Speed Control via FoPID-Controllers
Iqbal M. Batiha,Shaher Momani,Radwan M. Batyha,Iqbal H. Jebril,Duha Abu Judeh,Jamal Oudetallah 한국지능시스템학회 2024 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.24 No.1
This work aims to propose several designs for controlling the DC motor speed of a car. Suchmotor is broadly used in numerous applications like blowers, lathe machines, cranes, elevators,milling machines, fans, drilling rigs, etc. For achieving our aim, two optimization algorithms(Particle Swarm Optimization (PSO) and Bacterial Foraging Optimization (BFO)) will beexecuted to adjust the proposed controllers’ parameters. Accordingly, four Fractional-orderPID controllers (FoPID-controllers) will be formed in agreement with two types of schemes(Outstaloup’s and Continued Fraction Expansion (CFE) schemes), which will be used toapproximate the yielded Laplacian operators s±α, where 0 < α < 1.
Certain extended hypergeometric matrix functions of two or three variables
Praveen Agarwal,Rahul Goyal,Taekyun Kim,Shaher momani 장전수학회 2023 Advanced Studies in Contemporary Mathematics Vol.33 No.1
Certain extended hypergeometric matrix functions of two or three variables
Iqbal M. Batiha,Nashat Alamarat,Shameseddin Alshorm,O. Y. Ababneh,Shaher Momani 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.2
In this paper, we study a linear system of homogeneous commensurate incom- mensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.