Search

In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature rela- tions between the total space, the base space and the fibres on a submersion. In the present paper, we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. [ABSTRACT FROM AUTHOR]

Let n ≥ 1 be a fixed positive integer and R be a ring. A permuting n-additive map Ω : Rn → R is known to be permuting generalized n-derivation if there exists a permuting n-derivation Δ : Rn → R such that Ω(x1, x2, ⋯,xixi⋯,xn) = Ω(x1, x2, ⋯,xi,⋯xn)xi + xi Δ(x1, x2, ⋯,xi⋯xn) holds for all xi, xi ∈ R. A mapping δ : R → R defined by δ(x) = Δ(x, x, ⋯, x) for all x ∈ R is said to be the trace of Δ. The trace &# of can be defined in ω of Ω can be defined in the similar way. The main result of the present paper states that if R is a (n+1)!-torsion free semi-prime ring which admits a permuting n-derivation Δ such that the trace δ of Δ satisfies [[δ(x), x], x] ∈ Z (R) for all x ∈ R, then ͐ is commuting on R. Besides other related results it is also shown that in a n-torsion free prime ring if the trace ω of a permuting generalized n-derivation is centralizing on R, then ω is commuting on R. [ABSTRACT FROM AUTHOR]