Integrating Faith and Learning: Preparing Teacher Candidates to Serve Culturally and Linguistically Diverse Students

This essay examines how liberation theology and critical pedagogy inform the integration of faith and learning of a teacher educator who felt called to serve culturally and linguistically diverse students in the United States. The essay provides a brief cultural background of the educator’s journey from instructional assistant in an English learner program to teacher educator at a Christian University. The essay explains how liberation theology and critical pedagogy provide a coherent framework for preparing teacher candidates to work with English learners in public schools

Fractional Calculus of Variations for Double Integrals

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions.Comment: Submitted 07-Sept-2010; revised 25-Nov-2010; accepted 07-Feb-2011; for publication in Balkan Journal of Geometers and Its Applications (BJGA

Calculus of Variations with Classical and Fractional Derivatives

We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.Comment: This is a preprint of a paper whose final and definite form has been published in: Math. Balkanica 26 (2012), no 1-2, 191--202. It was first announced at the IFAC Workshop on Fractional Derivatives and Applications (IFAC FDA'2010), held in University of Extremadura, Badajoz, Spain, October 18-20, 2010; then subsequently at conference TMSF'201

The Generalized Fractional Calculus of Variations

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary optimality conditions of Euler-Lagrange type for the fundamental and isoperimetric problems, natural boundary conditions, and Noether type theorems.Comment: This is a preprint of a paper whose final and definite form will appear in Southeast Asian Bulletin of Mathematics (2014