In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Abstract In this paper we introduce a fractional variant of the characteristic function random variable. It exists on whole real line, and is uniformly continuous. We show that moments can be expressed in terms Riemann–Liouville integrals derivatives function. The are interest particular for distributions whose integer do not exist. Some illustrative examples also presented.

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

In this paper, under some super- and sub-linear growth conditions, we study the existence of positive solutions for a high-order Riemann–Liouville type fractional integral boundary value problem involving derivatives. Our analysis methods are based on fixed point index nonsymmetric property Green function. Additionally, provide valid examples to illustrate our main results.

Abstract In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo derivatives with initial integral conditions. Some new results on the existence uniqueness of solution for model are obtained as well Ulam stability solutions. Two examples provided to show applicability our results.

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generaliz...

In this paper, we study a new nonlinear sequential differential prob-
 lem with nonlocal integral conditions that involve convergent series. The
 problem involves two fractional order operators: Riemann-Liouville inte-
 gral, Caputo and derivatives. We prove an existence
 uniqueness result. Also, existence end our
 paper by presenting some illustrative examples.