Abstract The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with singular Caputo kernel and nonsingular Caputo–Fabrizio Atangana–Baleanu (ABC) kernel. proposed method based on the discrete Temimi–Ansari method, which combined three different schemes that are appropriate new derivative operators. technique used ...

We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of relations nth-weighted integrals and derivatives. As an application, mean value theorems operators are obtained. Direct corollaries allow one to obtain recent Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) ABC

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-know...

The outbreak of coronavirus (COVID-19) began in Wuhan, China, and spread all around the globe. For analysis said outbreak, mathematical formulations are important techniques that used for stability predictions infectious diseases. In given article, a novel system differential equations is considered under piecewise fractional operator Caputo Atangana–Baleanu. composed six ordinary (ODEs) differ...

Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous in a large variety of complex systems. The equivalent formulations terms Caputo or Riemann-Liouville fractional derivatives can be derived as continuum limits continuous-time random walks associated with the Mittag-Leffler relaxation Fourier modes, interpolating between short-time stretched exponential ...

This manuscript assesses a semi-analytical method in connection with new hybrid fuzzy integral transform and the Adomian decomposition via notion of fuzziness known as Elzaki (briefly, EADM). Moreover, we use aforesaid strategy to address time-fractional Fornberg–Whitham equation (FWE) under gH-differentiability by employing different initial conditions (IC). Several algebraic aspects Caputo fr...

In this study, two numerical methods—the variational iteration transform method (VITM) and the Adomian decomposition (ADM) method—were used to solve second- fourth-order fractional Boussinesq equations. Both methods are helpful in approximating non-linear problems effectively, easily, accurately. The Atangana–Baleanu operator ZZ were utilized derive solutions for equation. Two examples discusse...

Abstract The objective of this article is to incorporate the concept Ostrowski inequality with Atangana–Baleanu fractional integral operator. A novel identity for twice-differentiable functions established after a rigorous investigation several basic definitions and existing ideas related inequalities calculus. Following that, numerous Ostrowski-type are provided based on identity, which uses M...

Abstract In this paper, we study the following fractional differential equation involving Atangana-Baleanu-Caputo derivative: { A B C a D τ <m:m...