Browsing by Author "O'Regan, Donal"
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Article Citation Count: Baleanu, D., Mustafa, O.G., O'Regan, D. (2015). A Kamenev-type oscillation result for a linear (1+alpha)-order fractional differential equation. Applied Mathematics&Computation, 259, 374-378. http://dx.doi.org/10.1016/j.amc.2015.02.045A Kamenev-type oscillation result for a linear (1+alpha)-order fractional differential equation(Elsevier Science Inc., 2015) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, DonalWe investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1)Article Citation Count: Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal, "A Kamenev-Type Oscillation Result For a Linear (1+Alpha)-Order Fractional Differential Equation", Applied Mathematics and Computation, 259, pp. 374-378, (2015).A Kamenev-Type Oscillation Result For a Linear (1+Alpha)-Order Fractional Differential Equation(Elsevier Science, 2015) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal; 56389We investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1). (C) 2015 Elsevier Inc. All rights reserved.Article Citation Count: Baleanu, D., Mustafa, O.G., O'regan, D. (2011). A Nagumo-like uniqueness theorem for fractional differential equations. Journal of Physics A-Mathematical and Theoretical, 44(39). http://dx.doi.org/10.1088/1751-8113/44/39/392003A Nagumo-like uniqueness theorem for fractional differential equations(IOP Publishing Ltd, 30) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, DonalWe extend to fractional differential equations a recent generalization of the Nagumo uniqueness theorem for ordinary differential equations of first orderArticle Citation Count: Baleanu, D., Mustafa, O.G., O'regan, D. (2013). A uniqueness criterion for fractional differential equations with Caputo derivative. Nonlinear Dynamics, 71(4), 635-640. http://dx.doi.org/10.1007/s11071-012-0449-4A uniqueness criterion for fractional differential equations with Caputo derivative(Springer, 2013) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, DonalWe investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order alpha a(0,1). The differential operator is of Caputo type whereas the nonlinearity cannot be expressed as a Lipschitz function. Instead, the Riemann-Liouville derivative of this nonlinearity verifies a special inequality.Article Citation Count: Mohammed, Pshtiwan Othman;...et.al. (2022). "Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions", Mathematical Biosciences and Engineering, Vol.19, No.7, pp.7272-7283.Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions(2022) Mohammed, Pshtiwan Othman; O'Regan, Donal; Baleanu, Dumitru; Hamed, Y.S.; Elattar, Ehab E.; 56389We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ( CFR c0 r∇F ) (t) > -ϵ λ(θ - 1) - rF ∇ (c0 + 1) such that - rF ∇ (c0 + 1) ≥ 0 and ϵ > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of ϵ and θ.Article Citation Count: Tuan, Nguyen Huy...et al. (2020). "Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data", Journal of Computational and Applied Mathematics, Vol. 376.Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data(2020) Tuan, Nguyen Huy; Baleanu, Dumitru; Thach, Tran Ngoc; O'Regan, Donal; Can, Nguyen Huu; 56389In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction–diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically. © 2020 Elsevier B.V.Article Citation Count: Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal, "On a fractional differential equation with infinitely many solutions", Advances In Difference Equations, (2012)On A Fractional Differential Equation With İnfinitely Many Solutions(Springer International Publishing AG, 2012) Baleanu, Dumitru; Mustafa, Octavian G.; O'Regan, Donal; 56389We present a set of restrictions on the fractional differential equation , , where and , that leads to the existence of an infinity of solutions (a continuum of solutions) starting from . The operator is the Caputo differential operator.Article Citation Count: Mustafa, Octavian G.; O'Regan, Donal, "On an inverse scattering algorithm for the Camassa-Holm equation", Journal Of Nonlinear Mathematical Physics, Vol.15, No.3, pp.283-290, (2008).On an inverse scattering algorithm for the Camassa-Holm equation(Taylor&Francis, 2008) Mustafa, Octavian G.; O'Regan, DonalWe present a clarification of a recent inverse scattering algorithm developed for the Camassa-Holm equation.Article Citation Count: Agarwal, P...et al. (2018). On the solutions of certain fractional kinetic equations involving k-Mittag-Leffler function, Advances in Difference Equations.On the solutions of certain fractional kinetic equations involving k-Mittag-Leffler function(Springer Open, 2018) Agarwal, Ravi P.; Chand, M.; Baleanu, Dumitru; O'Regan, Donal; Jain, Shilpi; 56389The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function E-k,zeta,eta(gamma,rho)(center dot). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results.Article Citation Count: Tuan, Nguyen Huy...et al. (2020). "On well-posedness of the sub-diffusion equation with conformable derivative model", Communications in Nonlinear Science and Numerical Simulation, Vol. 89.On well-posedness of the sub-diffusion equation with conformable derivative model(2020) Tuan, Nguyen Huy; Ngoc, Tran Bao; Baleanu, Dumitru; O'Regan, Donal; 56389In this paper, we study an initial value problem for the time diffusion equation [Formula presented] on Ω × (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: • F=F(x,t), i.e., linear source term; • F=F(u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. • F=F(u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as – Time Ginzburg-Landau equations C∂βu/∂tβ+(−Δ)u=|u|μ−1u; – Time Burgers equations C∂βu/∂tβ−(u·∇)u+(−Δ)u=0; etc.Article Citation Count: Jarad, F. Mustafa, O.G., O'Regan, D. (2012). Positive solutions of some elliptic differential equations with oscillating nonlinearity. Complex Variables And Elliptic Equations, 57(6), 599-609. http://dx.doi.org/10.1080/17476933.2010.504836Positive solutions of some elliptic differential equations with oscillating nonlinearity(Taylor&Francis Ltd, 2012) Jarad, Fahd; Mustafa, Octavian G.; O'Regan, DonalWe discuss the occurrence of positive solutions which decay to 0 as vertical bar xj vertical bar ->+infinity the differential equation Delta u+f(x, u)+g(vertical bar x vertical bar)x . del u=0, vertical bar xj vertical bar>R>0, x is an element of R-n, where n >= 3, g is nonnegative valued and f has alternating sign, by means of the comparison method. Our results complement several recent contributions from Ehrnstrom and Mustafa [ M. Ehrnstrom, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal.
