Fractional variational calculus for nondifferentiable functions

We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints.Comment: Submitted 13-Aug-2010; revised 24-Nov-2010; accepted 28-March-2011; for publication in Computers and Mathematics with Application

Isoperimetric problems of the calculus of variations with fractional derivatives

In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.Comment: Submitted 02-Oct-2009; revised 30-Jun-2010; accepted 10-May-2011; for publication in the journal Acta Mathematica Scienti

Novel mutation in the mitochondrial transfer RNACys gene in a child

Mitochondrial DNA (mtDNA) disorders are an important group of genetic diseases presenting with a multifacet array of clinical manifestations. Highly energy-dependent tissues such as central nervous system and skeletal and cardiac muscles are commonly involved either as multisystem or as isolated organ disease. Characteristic symptoms include epilepsy, myopathy, deafness and ophthalmoplegia, all associated with point mutations in the mtDNA. Pathogenic mtDNA mutations can be heteroplasmic or homoplasmic. Heteroplasmic mutations are typically associated with mutations in mt-tRNA genes. Mutations in mt-tRNAs genes are responsible for the majority of the presentations of a mitochondrial disease being associated with marked clinical heterogeneity. Although tRNA-encoding genes make up only 9% of the entire mitochondrial genome, over 40% of all point mutations reported in the mtDNA are located in tRNA genes. Here, we present a child with vomiting episodes and migraine in whom we found a novel variant in the mitochondrial tRNACys gene

Higher-order infinite horizon variational problems in discrete quantum calculus

We obtain necessary optimality conditions for higher-order infinite horizon problems of the calculus of variations via discrete quantum operators.Comment: Submitted 11-May-2011; revised 16-Sept-2011; accepted 02-Dec-2011; for publication in Computers & Mathematics with Application

Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler-Lagrange equation for functionals where the lower and upper bounds of the integral are distinct of the bounds of the Caputo derivative is also proved. Then, the fractional isoperimetric problem is formulated with an integral constraint also containing Caputo derivatives. Normal and abnormal extremals are considered.Comment: Submitted 6/March/2010 to Communications in Nonlinear Science and Numerical Simulation; revised 12/July/2010; accepted for publication 16/July/201

The isoperimetric problem for Holderian curves

We prove a necessary stationary condition for non-differentiable isoperimetric variational problems with scale derivatives, defined on the class of H\"{o}lder continuous functions.Comment: 11 page

A General Backwards Calculus of Variations via Duality

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010; accepted for publication 08-July-201

Optimality conditions for the calculus of variations with higher-order delta derivatives

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.Comment: Submitted 26/Jul/2009; Revised 04/Aug/2010; Accepted 09/Aug/2010; for publication in "Applied Mathematics Letters

"Double trouble” or digenic disorder in Complex I deficiency

Complex I (CI) deficiency is a defect of OXPHOS caused by mutations in the mitochondrial or nuclear genomes. To date disease-causing mutations have been reported in all mitochondrial-encoded subunits and 22 nuclear genes. In about 50% of the patients no mutations are found, suggesting that undiscovered factors are an important cause of disease. In this study we report a consanguineous family from Southern Portugal with three affected children presenting with CI deficiency and 3-methylglutaconic aciduria type IV