A generalized fractional derivative (GFD) definition is proposed in this work. For a
differentiable function expanded by a Taylor series, we show that DαDβf (t)= Dα+ βf (t); 0< …

In this paper, a hybrid method called variational iteration transform method has been
implemented to solve fractional-order Navier–Stokes equation. Caputo operator describes …

An algorithm for approximating solutions to fractional differential equations (FDEs) in a
modified new Bernstein polynomial basis is introduced. Writing x→ x α (0< α< 1) in the …

In this paper, we present analytical-approximate solution to the time-fractional nonlinear
coupled Jaulent–Miodek system of equations which comes with an energy-dependent …

In this paper, we propose a neural network-based approach with an Extreme Learning
Machine (ELM) for solving fractional differential equations. The solution procedure for the …

In this paper, a collocation method based on the Bernstein polynomials is presented for the
fractional Riccati type differential equations. By writing t→ tα (0< α< 1) in the truncated …

In this study, we propose shifted fractional-order Jacobi orthogonal functions (SFJFs) based
on the definition of the classical Jacobi polynomials. We derive a new formula that explicitly …

In this paper, we have used the homotopy analysis method (HAM) to obtain approximate
solution of fractional integro-differential equations (FIDEs). Convergence of HAM is …

A new computational intelligence technique is presented for solution of non-linear quadratic
Riccati differential equations of fractional order based on artificial neural networks (ANNs) …

In this article, strength of fractional neural networks (FrNNs) is exploited to find the
approximate solutions of nonlinear systems based on Riccati equations of arbitrary order …