In order to develop certain fractional probabilistic analogues of Taylor’s theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution ...

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

<abstract><p>In this paper, we present a general formulation of the well-known fractional drifts Riemann-Liouville type. We state main properties these integral operators. Besides, study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving operators.</p></abstract>

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

In this article, we investigate partial integrals and derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral derivative order $\gamma = (p, q); p > 0,q 0$, functions are again corresponding to some iterated function system (IFS). Furthermore, discuss transforms

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D ax+ f1(t, x) = v(t) + f2(t, x), lim t→a+ J1−q a x(t) = b1, where D a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville dif...