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In this paper, the generalized differential transform method (GDTM) is used to solve certain class of nonlinear time-fractional diffusion equation. An efficient recurrence relation is obtained to solve this problem. Some numerical examples are given for different class of derivative orders which are analyzed numerically for the specified examples. [ABSTRACT FROM AUTHOR]

In this paper, we prove the stability of Hadamard homomorphisms and Hadamard derivations in Banach algebras. This is applied to investigate Hadamard isomorphisms between Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, new weighted Hermite-Hadamard type inequalities for differentiable preinvex and prequasiinvex functions are proved. These results generalize many results proved in earlier works for these classes of functions. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and M be an R-module. The aim of this paper is to introduce the notion of S-copure submodules and investigate some properties of this class of modules. We say that a submodule N of M is S-copure if there exists an s ∈ S such that s(N :M I) ⊆ N + (0 :M I) for every ideal I of R. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study some subclasses of p-valently analytic functions in the open unit disk U by applying the q-derivative operator and the fractional q-derivative operator in conjunction with the principle of subordination between analytic functions. For the Taylor-Maclaurin coefficients ... of each of these subclasses of p-valently analytic functions, we derive sharp bounds for the Fekete-Szegő functional given by ... Relevant connections of the results presented in this paper with those derived in earlier works are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a certain class H λ,a m,q (ξ,M) of normalized analytic functions of complex order connected with a q-analogue of integral operators. For this complex-order analytic function class, we determine a sufficient condition in terms of the coefficients, estimates for the coefficients and a maximization theorem concerning the coefficients. Various consequences and applications of our main results are also considered. A brief remark about the demonstrated equivalence of the q-calculus and the so-called (p,q)-calculus is also presented. [ABSTRACT FROM AUTHOR]

In this paper we introduce the classes Tn (p,λ,A,B) and Kn (p,λ,µ,m,A,B) and derive distortion inequalities of the functions belonging to class Kn (p,λ,µ,m,A,B). Further we apply to the (n,δ)- neighborhoods of functios in the class Kn (p,λ,µ,m,A,B). [ABSTRACT FROM AUTHOR]

In this paper, we present new kinds of reciprocal sums of finite products of general second order linear recurrences. In order to evaluate explicitly them by q-calculus, first we convert them into their q-notation and then use the methods of partial fraction decomposition and creative telescoping. [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete population model and obtain a couple of criteria to guarantee our model being stable, including the global attractor, the extreme stability, and the periodicity. [ABSTRACT FROM AUTHOR]

In this paper, by using umbral calculus and umbral algebra methods, we derive several interesting identities and relations related to the modified and unification of the Bernoulli, Euler and Genocchi polynomials and numbers and the generalized (β-) Stirling numbers of the second kind. We also give some applications and remarks related to these numbers and polynomials. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of solutions for a sequential fractional differential equation of arbitrary order ξ + 1; ξ ∊ (n-1, n), n ⩾ 2 with three-point nonlocal boundary conditions. We make use of standard tools of fixed point theory to establish our existence results. An illustrative example and some special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of solution for a multi-term arbitrary (fractional) order differential equation with some nonlocal and integral conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the statistical approximation properties of real and complex Post-Widder operators based on q-integers. We also obtain a Voronovskaya-type formula in statistical sense for these operators. [ABSTRACT FROM AUTHOR]

In this paper, for a general modification of the classical Sz´asz-Mirakjan-Kantorovich operators, we obtain many local approximation results including the classical cases. In particular, we obtain a Korovkin theorem, a Voronovskaya theorem, and some local estimates for these operators. [ABSTRACT FROM AUTHOR]