in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

Abstract In this paper, we first give the definition of Teodorescu operator related to $\mathcal{N}$ N matrix and discuss a series properties operator, such as uniform boundedness, Hölder continuity so on. Then propose Riemann boundary value problem operator. Finally, using intimate relationship corresponding...

Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann equations, the nonlinear one is based on the notion of circle patterns. We clarify the role of the rhombic condition in both theories: under this condition t...

theory for them, and they now turned to recap their earlier study of differential equations, upon which they went on to base their theory of elliptic functions. Not only did this free the theory of elliptic functions from any dependence on elliptic integrals with their confusing two-valued integrands, it meant that Briot and Bourquet denied themselves the chance to show how real integrals can b...

X iv :1 00 3. 45 53 v2 [ m at h. N T ] 6 J un 2 01 0 ON SOME LOWER BOUNDS OF SOME SYMMETRY INTEGRALS by G.Coppola Abstract. We study the “symmetry integral”, say If , of some arithmetic functions f : N → R; we obtain from lower bounds of If (for a large class of arithmetic functions f ) lower bounds for the “Selberg integral” of f , say Jf (both these integrals give informations about f in almo...