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Journal of Ocean Engineering and Science, 2019 This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.
L.A. Alhakim, A.A. Moussa
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SOLVABILITY FOR A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION [PDF]
Bulletin of the Australian Mathematical Society, 2009 AbstractIn this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem (BVP)where 1<α≤2,η∈(0,1),β∈ℝ=(−∞,+∞),βηα−1≠1,Dαis the Riemann–Liouville differential operator of orderα, andf:[0,1]×ℝ→ℝ is continuous,q(t):[0,1]→[0,+∞) is Lebesgue integrable.
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Advances in Difference Equations, 2018 In this paper, we investigate oscillatory and asymptotic properties for a class of fractional order dynamic equations on time scales, where the fractional derivative is defined in the sense of the conformable fractional derivative.
Qinghua Feng, Fanwei Meng
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Regularization of differential equations by fractional noise
Stochastic Processes and their Applications, 2002 Existence and uniqueness of a strong solution to the differential equation \[ X_t= x + \int _0^t b(s,X_s)\,ds + B^H_t, \quad t\geq 0, \] is established, where \(B^H_t\) is a fractional Brownian motion with the Hurst parameter \(H\in (0,1)\) and \(b(s,x)\) is a bounded Borel function with at most linear growth in \(x\) (for \(H\leq 1/2\)) or Hölder ...
Nualart, David, Ouknine, Youssef
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On matrix fractional differential equations
Advances in Mechanical Engineering, 2017 The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to
Adem Kılıçman, Wasan Ajeel Ahmood
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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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Averaged Systems of Stochastic Differential Equations with Lévy Noise and Fractional Brownian Motion
Fractal and FractionalIn some problems, partial differential equations are reduced to ordinary differential equations. In special cases, when incorporating randomness, equations can be reduced to systems of stochastic differential Equations (SDEs).
Tayeb Blouhi +6 more
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Fractal and FractionalThis paper is devoted to the general theory of systems of linear time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order is known
Sabir Umarov
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Impulsive Hilfer fractional differential equations
Advances in Difference Equations, 2018 Existence and controllability results for nonlinear Hilfer fractional differential equations are studied. Sufficient conditions for existence and approximate controllability for Sobolev-type impulsive fractional differential equations are established ...
Hamdy M. Ahmed +3 more
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Fredholm boundary-value problem for the system of fractional differential equations. [PDF]
Nonlinear Dyn, 2023 Boichuk O, Feruk V.
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