A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function that can be expanded by Taylor series, we show D^Elafa*D^Beta f(t)=D^(Elafa+Beta)f(t). GFD applied for some functions which investigate coincides with Caputo and Riemann-Liouville derivatives' results. The solutions of Riccati differential equation are simply obtained via GFD. comparison...

In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse transform. Further, find solution nonlinear reaction diffusion equation with by applying Fourier transforms.

Abstract The generalized Broer-Kaup-Kupershmidt (generalized BKK) isospectral problem, including the x-derivative of potential, is considered based on Lie algebra A1. The variational trace identity is extended to construct Hamiltonian structure of generalized BKK system. The Lie algebra A1 is extended to the non-semi-simple Lie algebra of 4 × 4 matrix form, from which a hierarchy of soliton equ...

In this paper, images of the tempered Ψ-Hilfer fractional integral and Ψ-Caputo derivative under generalized Laplace transform are derived. The results applied to find a solution an initial value problem for nonhomogeneous linear differential equation with order α n− 1 <α<n N. An illustrative example is given 0 <α<1 comparing solutions same but different tempering Ψ.