Sufficient conditions for extremum of fractional variational problems

Sufficient conditions for extremum of fractional variational problems are formulated with the help Caputo derivatives. The Euler–Lagrange equation is defined in sense and Jacobi derived using this. Again, Wierstrass integral considered functional obtained from transversality conditions. Further, Taylor’s series expansion derivatives integral, Legendre’s sufficient condition problem established. Finally, a suitable counterexample presented to justify efficacy fresh findings.