Browsing by Author "Mustafa, Octavian G."
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Article Citation Count: Abdeljavad, T...et al. (2010). A fite type result for sequental fractional differintial equations. Dynamic System and Applications, 19(2), 383-394.A fite type result for sequental fractional differintial equations(Dynamic Publisher, 2010) Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Mustafa, Octavian G.; Trujillo, J. J.Given the solution f of the sequential fractional differential equation aD(t)(alpha)(aD(t)(alpha) f) + P(t)f = 0, t is an element of [b, a], where -infinity < a < b < c < + infinity, alpha is an element of (1/2, 1) and P : [a, + infinity) -> [0, P(infinity)], P(infinity) < + infinity, is continuous. Assume that there exist t(1),t(2) is an element of [b, c] such that f(t(1)) = (aD(t)(alpha))(t(2)) = 0. Then, we establish here a positive lower bound for c - a which depends solely on alpha, P(infinity). Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equationsArticle 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: Baleanu, D., Mustafa, O.G., Agarwal, R.P. (2010). An existence result for a superlinear fractional differential equation. Applied Mathematics Letters, 23(9), 1129-1132. http://dx.doi.org/10.1016/j.aml.2010.04.049An existence result for a superlinear fractional differential equation(Pergamon-Elsevier Science Ltd, 2010) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.We establish the existence and uniqueness of solution for the boundary value problem (0)D(t)(alpha)(x') + a(t)x(lambda) = 0, t > 0, x' (0) = 0, lim(t ->+infinity) x(t) = 1, where (0)D(t)(alpha) designates the Riemann-Liouville derivative of order alpha epsilon (0, 1) and lambda > 1. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden-Fowler equationsArticle Citation Count: Bleanu, D.; Mustafa, O.G.; Agarwal, R.P.,"Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations",Vol. 62, No. 3, pp. 1492-1500, (2011).Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389We establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0Article Citation Count: Baleanu, D...et al. (2011). Asymptotic integration of (1+alpha)-order fractional differential equations. Computers&Mathematics With Applications, 62(3), 1492-1500. http://dx.doi.org/10.1016/j.camwa.2011.03.021Asymptotic integration of (1+alpha)-order fractional differential equations(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0.Article Citation Count: Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P. " Asymptotic integration of (1+alpha)-order fractional differential equations", Computers & Mathematics With Applications, Vol. 62, No. 3, pp. 1492-1500, (2011)Asymptotic Integration of (1+Alpha)-Order Fractional Differential Equations(Pergamon-Elsevier Science LTD, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation Count: Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P. (2011). "Asymptotic integration of (1+alpha)-order fractional differential equations", Computers & Mathematics With Applications, Vol. 62, no. 3, pp. 1492-1500.Asymptotic integration of (1+alpha)-order fractional differential equations(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation Count: Baleanu, D...et al. (2011). Asymptotic integration of some nonlinear differential equations with fractional time derivative. Journal of Physics A-Mathematical and Theoretical, 44(5). http://dx.doi.org/ 10.1088/1751-8113/44/5/055203Asymptotic integration of some nonlinear differential equations with fractional time derivative(IOP Publishing Ltd, 2011) Baleanu, Dumitru; Agarwal, Ravi P.; Mustafa, Octavian G.; Cosulshci, MirelWe establish that, under some simple integral conditions regarding the nonlinearity, the (1 + alpha)-order fractional differential equation (0)D(t)(alpha) (x') + f (t, x) = 0, t > 0, has a solution x is an element of C([0, +infinity), R) boolean AND C(1)((0, +infinity), R), with lim(t SE arrow 0) [t(1-alpha)x'(t)] is an element of R, which can be expanded asymptotically as a+bt(alpha)+O(t(alpha-1)) when t ->+infinity for given real numbers a, b. Our arguments are based on fixed point theory. Here, (0)D(t)(alpha) designates the Riemann-Liouville derivative of order alpha is an element of (0, 1)Article Citation Count: Baleanu, D., Mustafa, O.G., Agarwal, R.P. (2010). Asymptotically linear solutions for some linear fractional differential equations. Abstract and Applied Analysis. http://dx.doi.org/ 10.1155/2010/865139Asymptotically linear solutions for some linear fractional differential equations(Hindawi Publishing Corporation, 2010) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.We establish here that under some simple restrictions on the functional coefficient a(t) the fractional differential equation 0D(t)(alpha)[tx' - x + x(0)] + a(t)x = 0, t > 0, has a solution expressible as ct + d + o(1) for t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of order alpha is an element of (0, 1) and c, d is an element of RArticle 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: Baleanu, D...et al. (2011). On L-p-solutions for a class of sequential fractional differential equations. Applied Mathematics&Computation, 218(5), 2074-2081. http://dx.doi.org/ 10.1016/j.amc.2011.07.024On L-p-solutions for a class of sequential fractional differential equations(Elsevier Science Inc., 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.Under some simple conditions on the coefficient a( t), we establish that the initial value problem ((0)D(t)(alpha)x)' + a(t)x = 0; t > 0; lim(t SE arrow 0)[t(1-alpha)x(t)] = 0 has no solution in L-p((1, +infinity), R), where p-1/p > alpha > 1/p and D-0(t)alpha designates the Riemann-Liouville derivative of order alpha Our result might be useful for developing a non-integer variant of H. Weyl's limit-circle/limit-point classification of differential equations. (C) 2011 Elsevier Inc. All rights reserved.Article Citation Count: Baleanu, D., Mustafa, O.G. (2009). On the asymptotic integration of a class of sublinear fractional differential equations. Journal of Mathematical Physics, 50(12). http://dx.doi.org/10.1063/1.3271111On the asymptotic integration of a class of sublinear fractional differential equations(Amer Inst Physics, 2009) Baleanu, Dumitru; Mustafa, Octavian G.We estimate the growth in time of the solutions to a class of nonlinear fractional differential equations D(0+)(alpha)(x-x(0))=f(t,x) which includes D(0+)(alpha)(x-x(0))=H(t)x(lambda) with lambda is an element of(0,1) for the case of slowly decaying coefficients H. The proof is based on the triple interpolation inequality on the real line and the growth estimate reads as x(t)=o(t(a alpha)) when t ->+infinity for 1>alpha>1-a>lambda>0. Our result can be thought of as a noninteger counterpart of the classical Bihari asymptotic integration result for nonlinear ordinary differential equations. By a carefully designed example we show that in some circumstances such an estimate is optimalArticle Citation Count: Baleanu, D., Mustafa, O.G. (2010). On the global existence of solutions to a class of fractional differential equations. Computers&Mathematics With Applications, 59(5), 1835-1841. http://dx.doi.org/10.1016/j.camwa.2009.08.028On the global existence of solutions to a class of fractional differential equations(Pergamon-Elsevier Science Ltd, 2010) Baleanu, Dumitru; Mustafa, Octavian G.We present two global existence results for an initial value problem associated to a large class of fractional differential equations. Our approach differs substantially from the techniques employed in the recent literature. By introducing an easily verifiable hypothesis, we allow for immediate applications of a general comparison type result from [V. Lakshmikantham, AS. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. TMA 69 (2008), 2677-2682]Article Citation Count: Baleanu, D., Mustafa, O.G., Agarwal, R.P. (2010). On the solution set for a class of sequential fractional differential equations. Journal of Physics A-Mathematical and Theoretical, 43(38). http://dx.doi.org/10.1088/1751-8113/43/38/385209On the solution set for a class of sequential fractional differential equations(IOP Publishing Ltd, 2010) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.We establish here that under some simple restrictions on the functional coefficient a(t) the solution set of the fractional differential equation ((0)D(t)(alpha)x)' + a(t) x = 0 splits between eventually small and eventually large solutions as t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of the order alpha is an element of (0, 1)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.
