1 Professor and author of correspondence, Phone: +91 3222-283084, Fax: +91 3222 255303, Email: [email protected] ABSTRACT A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Op...

The principal motivation of this paper is to establish a new integral equality related k-Riemann Liouville fractional operator. Employing equality, we present several inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard inequality. Additionally, some novel cases the established results different kinds derived. This sums up Riemann–Liouville and Hermit...

In [10] a “direct” stochastic transfer principle was introduced, which represented multiple integrals with respect to fractional Brownian motion in terms of multiple integrals with respect to standard Brownian motion. The method employed in [10] involved an operator Γ (n) H , mapping a class of functions LH to L 2. However, the operator does not map LH onto L 2. Hence Γ (n) H is not invertible....

Here we prove fractional representation formulae involving generalized fractional derivatives, Caputo fractional derivatives and Riemann–Liouville fractional derivatives. Then we establish Poincaré, Sobolev, Hilbert–Pachpatte and Opial type fractional inequalities, involving the right versions of the abovementioned fractional derivatives.

We investigate the existence of positive solutions a Riemann-Liouville fractional differential equation with sequential derivatives, parameter and nonnegative singular nonlinearity, supplemented integral-multipoint boundary conditions which contain derivatives various orders Riemann-Stieltjes integrals. Our general cover some symmetry cases for unknown function. In proof our main result, we use...

The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and Vega and Bourgain to the initial-boundary setting. The approach consists of replacing the initial-boundary problem by a forced initial value problem. The forcing is selected to satisfy the boundary condition by inverti...

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...

We correct a recent result concerning the fractional derivative at extreme points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extreme points.