scholarly journals Solving Fractional Variational Problem Via an Orthonormal Function

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Akram Kheirabadi ◽  
Asadollah Mahmoudzadeh Vaziri ◽  
Sohrab Effati
Keyword(s):  
Variational Problem ◽  
Fractional Variational Problem

scholarly journals Fractional Variational Problems of Euler-Lagrange Equations with Holonomic Constrained Systems

2016 ◽  
Vol 8 (3) ◽  
pp. 60 ◽  
Author(s):  
Eyad Hasan Hasan
Keyword(s):  
Variational Problem ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Constrained Systems ◽  
Lagrange Equations ◽  
Integer Order ◽  
Fractional Variational Problems ◽  
Fractional Variational Problem ◽  
Problem Of Lagrange

<p class="1Body">In this paper, we examined the fractional Euler-Lagrange equations for Holonomic constrained systems. The Euler-Lagrange equations are derived using the fractional variational problem of Lagrange. In addition, we achieved that the classical results were obtained are agreement when fractional derivatives are replaced with the integer order derivatives. Two physical examples are discussed to demonstrate the formalism.</p>

About Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives

2005 ◽  
Author(s):  
Dumitru Baleanu ◽  
Sami I. Muslih
Keyword(s):  
Variational Problem ◽  
Path Integral ◽  
Fractional Derivatives ◽  
Mechanical Systems ◽  
Lagrangian Formulation ◽  
Dinger Equation ◽  
Classical Fields ◽  
Fractional Variational Problem ◽  
Problem Of Lagrange

Recently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal’s approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schro¨dinger equation is presented.

scholarly journals A Generalization of a Fractional Variational Problem with Dependence on the Boundaries and a Real Parameter

2021 ◽  
Vol 5 (1) ◽  
pp. 24
Author(s):  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Variational Problem ◽  
Fractional Derivatives ◽  
Variational Calculus ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Caputo Fractional Derivatives ◽  
Independent Variable ◽  
Left And Right ◽  
Necessary And Sufficient ◽  
Fractional Variational Problem

In this paper, we present a new fractional variational problem where the Lagrangian depends not only on the independent variable, an unknown function and its left- and right-sided Caputo fractional derivatives with respect to another function, but also on the endpoint conditions and a free parameter. The main results of this paper are necessary and sufficient optimality conditions for variational problems with or without isoperimetric and holonomic restrictions. Our results not only provide a generalization to previous results but also give new contributions in fractional variational calculus. Finally, we present some examples to illustrate our results.

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