2011, Vol 12, No 2
http://hdl.handle.net/123456789/10569
Thu, 18 Apr 2019 22:20:12 GMT2019-04-18T22:20:12ZGeneralized Leibniz rule for an extended fractional derivative operator with applications to special functions
http://hdl.handle.net/123456789/10580
Generalized Leibniz rule for an extended fractional derivative operator with applications to special functions
Gaboury, S.; Tremblay, R.; Fugère, B. J.
Recently an extended operator of fractional derivative related to a generalized beta function has been used in order to obtain some generating relations involving extended hypergeometric functions [19]. In this paper, an extended fractional derivative operator with respect to an arbitrary regular and univalent function based on the Cauchy integral formula is defined. This is done to compute the extended fractional derivative of the function log z and principally, to obtain a generalized Leibniz rule. Some examples involving special functions are given. A representation of the extended fractional derivative operator in terms of the classical fractional derivative operator is also determined by using a result of A.R. Miller [12].
URL: http://sjam.selcuk.edu.tr/sjam/article/view/310
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/123456789/105802011-01-01T00:00:00ZOn residual transcendental extensions of a valuation with rankv = 2
http://hdl.handle.net/123456789/10579
On residual transcendental extensions of a valuation with rankv = 2
Özturk, Burcu; Öke, Figen
Let v=v??v? be a valuation of a field K with rankv=2. In this paper a residual transcendental extension w=w??w? of v to K(x) is studied where w? and w? are the residual extensions of v? and v? respectively. A characterization of lifting polynomials is given and the constants w_{(K,v)}(c), ?_{(K,v)}(c), ?_{(K,v)}(c) are defined for c, where (c,?)?K_{v} is the minimal pair defining w.
URL: http://sjam.selcuk.edu.tr/sjam/article/view/309
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/123456789/105792011-01-01T00:00:00ZΔm-ideal convergence
http://hdl.handle.net/123456789/10578
Δm-ideal convergence
Gümüş, Hafize Gök; Nuray, Fatih
Statistical convergence has several applications in different fields of Mathematics: Number theory, trigonometric series, summability theory, probability theory, measure theory, optimization and approximation theory. The notion of ideal convergence corresponds to a generalization of the statistical convergence. In this paper, we define the ?^{m}(c_{I}) spaces by using generalized sequence spaces and ideal convergence. Furthermore we establish some topological results and give inclusion relation between ?^{m}(w_{p}^{T})-convergence and ?^{m}-ideal convergence.
URL: http://sjam.selcuk.edu.tr/sjam/article/view/308
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/123456789/105782011-01-01T00:00:00ZExistence of solutions of BVPs for nonlinear difference equations: non-resonance case
http://hdl.handle.net/123456789/10577
Existence of solutions of BVPs for nonlinear difference equations: non-resonance case
Liu, Yuji
Sufficient conditions for the existence of solutions of the following boundary value problem for nonlinear difference equation{<K1.1/>?<K1.1 ilk="MATRIX" ><K2.1/><K2.2/><K2.3/></K1.1><K2.1 ilk="MATRIX" >x(t+2k)-?_{i=0}^{2k-1}a_{i}x(t+i)=f(t,x(t),x(t+1),?,x(t+2k-1)),t?[0,T-1],</K2.1><K2.2 ilk="MATRIX" >x(i)=A_{i},i?[0,k-1],</K2.2><K2.3 ilk="MATRIX" >x(T+2k-1-i)=B_{i},i?[0,k-1]</K2.3>at non-resonance case are established. Examples are given to show the efficiency of the result in this paper.
URL: http://sjam.selcuk.edu.tr/sjam/article/view/307
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/123456789/105772011-01-01T00:00:00Z