Search

We first introduce the concept of fractional operators and pseudo-analysis. Then we present new versions of H¨older, Minkowski and reverse Minkowski inequalities via ψ -Riemann-Liouville-Mittag-Leffler pseudo-fractional integral on a semiring ([a,b],⊕,⊙). [ABSTRACT FROM AUTHOR]

Basic theory on a class of initial value problem of some fractional differential equation involving Riemann-Liouville differential operators is discussed by employing the classical approach from the work of Lakshmikantham and A. S. Vatsala (2008). The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered. Our work employed recent literature from the work of (Lakshmikantham and A. S. Vatsala, (2008)).

By using the Guo-Krasnoselskii's fixed point theorem, we investigate the existence of positive solutions for a non-autonomous fractional differential equations with integral boundary conditions of fractional order α ∈ (2, 3] in an ordered Banach space. The Fredholm integral equation has an important role in this article. Some examples are presented to illustrate the efficiency of the obtained results. [ABSTRACT FROM AUTHOR]

Minkowski's inequality is one of the most famous inequalities in mathematics, and has many applications. In this paper, we give Minkowski's inequality for generalized variational integrals that are based on a supermultiplicative function. Our results include previous results about fractional integral inequalities of Minkowski's type. [ABSTRACT FROM AUTHOR]

In this paper, we discuss existence and uniqueness of solutions to nonlinear frac-tional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The non-linear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In the present paper we discuss the existence of positive solutions in the case of multi-term non-autonomous fractional differential equations with polynomial coefficients; the constant coefficient case has been studied in[2]. We consider the equation Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. We state various conditions on f and pj's under which this equation has: positive solutions, a unique solution which is positive, and a unique solution which may not be positive. [ABSTRACT FROM AUTHOR]