In [12] we defined a class of functions called Type-2 Time Bounds (henceforth T2TB) for clocking the Oracle Turing Machine (OTM) in order to capture the long missing notion of complexity classes at type-2. In the present paper we further advance the type-2 complexity theory under our notion of type-2 complexity classes. We have learned that the theory is highly sensitive to how the oracle answe...

The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively recent past. Suitable fixed point theorem to be selected study boundary value due properties exhibited difference operators. This article aims at investigating stability results sense Hyers and Ulam with application Mittag–Leffler function hybrid or...

In this paper, taking into account the recent contractive technique we present a new result of Presic type fixed point theorems. Then, provide comparative example to put forth validity our theoretical result. Finally, considering special case main theorem, give some existence results for second order two boundary value problems.

The authors obtain existence and uniqueness results for a nonlinear fractional pantograph boundary value problem containing variable order Hadamard derivative. This type of model is appropriate applications involving processes that occur in strongly anomalous media. They also derive generalized Lyapunov-type inequality the considered. Their are obtained by calculus Krasnosel’skii’s fixed point ...

In this article, we discuss the existence and uniqueness of solution to fractional order ordinary and delay differential equations. We apply our results on the single species model of Lotka Volterra type. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle and then Krasnoselskii’s fixed point theorem to sh...

In [1], Constantine proposed that a variant of the codes constructed in Theorem 1 might be a useful substitute for Hadamard matrices at orders where no Hadamard matrix is known to exist. His main result is a plug-in construction for codes of order 4q with 8q codewords and minimum distance 2q−2 using a Goethals-Seidel type array. He provides component matrices for odd prime powers q. Theorem 1 s...

Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem to an isomorphism theorem. Our result relates injectivity theorems to a certain homology localization of groups. In order to give a concrete combinatorial de...