162 citations · 193 across the 8 of their papers we have counts for
10 papers
Bridging Algebra and Nature: Toward a Deformable 3D Hyper-complex framework for Modeling Dynamic Systems
Abdon Atangana
In this paper, we present a new hypercomplex number system, Trinition, that has an unusual structure of commutativity, noncommutativity, nonassociativity, and deformability.
On the formulation of fractional Adams-Bashforth method with Atangana-Baleanu-Caputo derivative to model chaotic problems
Kolade M. Owolabi, Abdon Atangana
Mathematical analysis with numerical application of the newly formulated fractional version of the Adams-Bashforth method using the Atangana-Baleanu derivative which has nonlocal a…
New Two Step Laplace Adam-Bashforth Method for Integer an Non integer Order Partial Differential Equations
Rodrigue Gnitchogna Batogna, Abdon Atangana
This paper presents a novel method that allows to generalise the use of the Adam-Bashforth to Partial Differential Equations with local and non local operator. The Method derives a…
New numerical approach for fractional differential equations
Abdon Atangana, Kolade M. Owolabi
In the present case, we propose the correct version of the fractional Adams-Bashforth methods which take into account the nonlinearity of the kernels including the power law for th…
Certain Fractional Kinetic Equations Involving Generalized k-Bessel Function
Praveen Agarwal, Shilpi Jain, Abdon Atangana +2
We develop a new and further generalized form of the fractional kinetic equation involving generalized k-Bessel function. The manifold generality of the generalized k-Bessel functi…
New numerical scheme of Atangana-Baleanu fractional integral: an application to groundwater flow within leaky aquifer
J. D. Djida, I. Area, A. Atangana
Many physical problems can be described using the integral equations known as Volterra equations. There exists quite a number of analytical methods that can handle these equations…
More generalized groundwater model with space-time Caputo Fabrizio fractional differentiation
J-D Djida, A. Atangana
We prove existence and uniqueness of the flow of water within a confined aquifer with fractional diffusion in space and fractional time derivative in the sense of Caputo-Fabrizio.…
Numerical computation of a fractional derivative with non-local and non-singular kernel
J. D. Djida, I. Area, A. Atangana
A numerical scheme for solving fractional initial value problems involving the Atangana-Baleanu fractional derivative is presented. Some examples for the proposed method are includ…
Derivative with two fractional orders: New door of investigation toward revolution in fractional calculus
Abdon Atangana
In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definit…
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana, Dumitru Baleanu
In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve…