# Fractional Calculus and Applied Analysis

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 3-18

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 31-55

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 110-124

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 19-30

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 56-79

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 80-93

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 138-155

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 125-137

Fractional Calculus and Applied Analysis > 2011 > 14 > 1 > 94-109

*and*the order of the derivation. The Euler-Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive...

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 284-300

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 247-259

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 164-200

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 317-320

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 201-232

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 260-283

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 301-316

*α*-times

*C*-regularized resolvent families (

*α*> 1) in sequentially complete locally convex spaces. We also consider the growth order of constructed solutions.

Fractional Calculus and Applied Analysis > 2011 > 14 > 2 > 233-246

*d*-plane Radon transform, namely

*R*, on the

*n*-dimensional (flat) torus. The transformation

*R*is obtained by integrating a suitable function

*f*over all

*d*-dimensional geodesics (

*d*-planes in the torus). We specially establish an explicit inversion formula of

*R*and we give a characterization of the image, under the

*d*-plane Radon transform, of the space of smooth functions on the...

Fractional Calculus and Applied Analysis > 2011 > 14 > 3 > 411-417