Numerical calculation of the fractional integrals and derivatives is the code to search fractional calculus and solve fractional differential equations. The exact solutions to fractional differential equations are ...

In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)- dimensional fractional-order Fokas ...

We apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the ...

The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our ...

By using an interpolation approach, we recognize Boyd-Wong and Matkowski type contractions and we prove the related fixed point theorems in the class of metric spaces. The obtained results are supported by some examples. ...

This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also ...

In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of ...

This research paper is devoted to investigating two classes of boundary value problems for nonlinear Atangana-Baleanu-type fractional differential equations with Atangana-Baleanu fractional integral conditions. The applied ...