Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional deri...

In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffl...

A class of second order approximations, called the weighted and shifted Grünwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coe...

In this paper, we consider a time-dependent diffusion problem with two-sided Riemann-Liouville fractional derivatives. By introducing a fractional-order flux as auxiliary variable, we establish the saddle-point variational formulation, based on which we employ a locally conservative mixed finite element method to approximate the unknown function, its derivative and the fractional flux in space ...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann–Liouville fractional ...

A system of nonlinear fractional differential equations with the Riemann–Liouville derivative is considered. Lipschitz stability in time for studied defined and studied. This connected singularity at initial point. Two types derivatives Lyapunov functions among are applied to obtain sufficient conditions property. Some examples illustrate results.

The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. case electric circuits, ruled by non-integer derivatives capacitors with fractional dielectric permittivity, fairly natural frame relevant applications. We techniques, generalized exponential obtain suitable solutions for this t...

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in Sobolev spaces. Our provides feasible extension classical Caputo Riemann–Liouville within spaces orders, including negative ones. approach enables unified treatment for calculus equations. We formulate initial value problems ordinary equations boundary partial to pr...

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point groups and the corresponding optimal subgroups are determined. Then, similarity reduction performed given equation some explicit solutions derived. asymptotic behaviours for also discussed. Through concept nonlinear self-adjointness...

In this study, we establish a novel version of Hermite-Hadamard inequalities through neoteric generalized Riemann-Liouville fractional integrals (RLFIs). For functions with the convex absolute values derivatives, create variety midpoint and trapezoid form inequalities, including RLFIs. Moreover, multiple can be produced as special cases findings study.