the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann–Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and convexity, we prove existence of solutions. AMS Subject Classifications: 26A33, 49J05.

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

We prove a Noether’s theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.

This paper presents improvements of some Opial-type inequalities involving the RiemannLiouville, Caputo and Canavati fractional derivatives, and presents some new Opial-type inequalities. Mathematics subject classification (2010): 26A33, 26D15.

In the paper under review, we analyze a class of abstract distributionally chaotic (multi-term) fractional differential equations in Banach spaces, associated with use of the Caputo fractional derivatives. AMS Mathematics Subject Classification (2010): 47A16, 47D03, 47D06, 47D99

There has been a recent increase in interest in the use of distributed order differential equations (particularly in the case where the derivatives are given in the Caputo sense) to model various phenomena. Recent papers have provided insights into the numerical approximation of the solution, and some results on existence and uniqueness have been proved. In each case, the representation of the ...

Numerical evaluations of Caputo fractional derivatives for scattered noisy data is an important problem in scientific research and practical applications. Fractional derivatives have been applied recently to the numerical solution of problems in fluid and continuum mechanics. The Caputo fractional derivative of order α is given as follows f (t) = 1 Γ(1− α) ∫ t 0 f (s) (t− s)α ds, 0 < α < 1 The ...

In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to non-symmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space H α/2 0 (0, 1) but the ...