Fast Hybrid Schemes for Fractional Riccati Equations (Rough is not so Tough)
, 2020 We solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients. These equations arise, e.g., in fractional Heston stochastic volatility models, that have received great attention in the recent financial ...
Gilles, Pagès +2 more
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Results in Physics, 2018 In this paper, we constructed a travelling wave solution for space-time fractional nonlinear partial differential equations by using the modified extended Tanh method with Riccati equation.
Muhannad A. Shallal +2 more
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Exact Solution of Two-Dimensional Fractional Partial Differential Equations
Fractal and Fractional, 2020 In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati ...
Dumitru Baleanu, Hassan Kamil Jassim
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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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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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Oscillation criteria for nonlinear fractional differential equation with damping term
Open Physics, 2016 In this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a
Bayram Mustafa +2 more
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Wave solution behaviors for fractional nonlinear fluid dynamic equation and shallow water equation [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 The behaviors of wave solutions of the fractional nonlinear space-time Sharma-Tasso-Olever equation and the fractional nonlinear space-time Estevez-Mansfield-Clarkson equation, representing a fluid dynamics equation and a shallow water equation ...
Weerachai Thadee +3 more
doaj
Lie systems: theory, generalisations, and applications [PDF]
, 2011 Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the ...
J. De Lucas +3 more
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The Exact Solution of the Fractional Burger’s Equation using the Modified Homogeneous Balance Method
Scientific AfricanIn this paper, the Modified Homogeneous Balance Method, which is embedded with a fractional Riccati equation, is used to find exact solutions to the fractional Burger’s equation.
Francis Tuffour +3 more
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On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation [PDF]
, 2014 We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of integrations on each
Pietrzkowski, Gabriel
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