in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

In this present work, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the direct algebraic method are employed for constructing the exact complex solutions of non-linear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. Reference to this paper should be made as follows: Taghiz...

and Applied Analysis 3 Let Γ(⋅) denote the gamma function. For any positive integer n and real number θ (n − 1 < θ < n), there are different definitions of fractional derivatives with order θ in [8]. During this paper, we consider the left, (right) Caputo derivative and left (right) Riemann-Liouville derivative defined as follows: (i) the left Caputo derivative: C 0 D θ t V (t) = 1 Γ (n − θ) ∫ ...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

In this paper, a time-fractional derivative nonlinear Schrödinger equation involving the Riemann–Liouville fractional is investigated. We first perform Lie symmetry analysis of equation, and then derive reduced equations under admitted optimal-symmetry system. Moreover, with invariant subspace method, several exact solutions for their figures are presented. Finally, new conservation theorem app...

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.