In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

In this article, we get solutions of some integral inequalities Hermite-Hadamard type and using the approach ($\psi$,$h$)-Convex function by way Riemann-Liouville Fractional integrals Katugampola operators.

In this paper, a novel image denoising algorithm named fractional integral image denoising algorithm (FIIDA) is proposed, which based on fractional calculus Riemann-Liouville definition. The structures of n*n fractional integral masks of this algorithm on the directions of 135 degrees, 90 degrees, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees are constructed and d...

In this paper we consider the integral equation of fractional order in sense of Riemann-Liouville operator u(t) = a(t)I[b(t)u(t)] + f(t) with m ≥ 1, t ∈ [0, T ], T < ∞ and 0 < α < 1. We discuss the existence, uniqueness, maximal, minimal and the upper and lower bounds of the solutions. Also we illustrate our results with examples. Full text

The quantum analogs of the derivatives with respect to coordinates qk and momenta pk are commutators with operators Pk and Qk. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for an...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract This article investigates a boundary value problem of Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary condi...

*Correspondence: [email protected] 1Luleå University of Technology, Luleå, 971 87, Sweden 2Narvik University College, P.O. Box 385, Narvik, 8505, Norway Full list of author information is available at the end of the article Abstract We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n ∈ N. Some new Hardy-type inequalities for this operator are proved and dis...

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. We also show that a fractional Brownian motion and the related Riemann–Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of o...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...