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Solution of Nonlinear Space-Time Fractional Differential Equations Using the Fractional Riccati Expansion Method [PDF]
Mathematical Problems in Engineering, 2013 The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered.
Emad A.‐B. Abdel‐Salam +1 more
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On the numerical solution of fractional Riccati differential equations
Malaya Journal of Matematik, 2020 Ashitha P.A., M. C. Ranjini
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Analysis of solitary wave solutions in the fractional-order Kundu–Eckhaus system [PDF]
Scientific ReportsThe area of fractional partial differential equations has recently become prominent for its ability to accurately simulate complex physical events. The search for traveling wave solutions for fractional partial differential equations is a difficult task,
Saleh Alshammari +6 more
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International Journal of Differential Equations, 2021 In this paper, a class of fractional order differential equation expressed with Atangana–Baleanu Caputo derivative with nonlinear term is discussed.
Meryeme Hassouna +2 more
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Transform of Riccati equation of constant coefficients through fractional procedure [PDF]
, 2003 We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as ...
A L Madue o +8 more
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Enhancing the Accuracy of Solving Riccati Fractional Differential Equations
Fractal and Fractional, 2022 In this paper, we solve Riccati equations by using the fractional-order hybrid function of block-pulse functions and Bernoulli polynomials (FOHBPB), obtained by replacing x with xα, with positive α. Fractional derivatives are in the Caputo sense. With the help of incomplete beta functions, we are able to build exactly the Riemann–Liouville fractional ...
Antonela Toma +2 more
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THE RICCATI EQUATION WITH VARIABLE HEREDITY [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2017 We consider the Riccati differential equation with a fractional derivative of variable order. The introduction of a derivative of a fractional variable order into the initial equation determines the property of the medium — the memory effect or the ...
Tvyordyj D. A.
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Matematika, 2019 Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional.
Muhamad Deni Johansyah +4 more
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Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System
Applied Sciences, 2021 The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected.
Akihiro Takeshita +3 more
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A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement [PDF]
, 2012 A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems ...
Das, Saptarshi +3 more
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