In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

In this study, we develop a theory for the nonlocal hybrid boundary value problem fractional integro-differential equations featuring Atangana–Baleanu derivatives. The corresponding integral equation is presented. Then, establish existence results using Dhage’s fixed point theorem sum of three operators. We also offer additional exceptional cases and similar outcomes. order to demonstrate verif...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....