Investigation of nonlinear fractional delay differential equation via singular fractional operator

The present research work is basically devoted to construction of a fractional order differential equation with time delay. Initially, integral representation is given to solution of the underline problem. Afterwards, operator form of solution is studied under some auxiliary hypothesis. Since uniqueness of solution is required, therefore we also provide results for exploring the uniqueness of solution for the underlying model. Using Lebesgue dominated convergence theorem and some other results from analysis, this work provides results devoted to existence of at least one solution. Also, for investigating the nature of solution for the proposed model, we study different kind of stability analysis. These stability related results show, how the solution behave with time. At the end of the article, we illustrate the obtained results via some examples.

Stability of Atangana - Baleanu Fractional Order Differential Equation with Numerical Approximation

The field of Fractional calculus is more useful to understand the real-world phenomena. In this article, a nonlinear fractional order differential equation with Atangana-Baleanu operator is considered for analysis. Sufficient conditions under which a solution exists and uniqueness are presented using Banach fixed-point theorem method. The well-established Adams-Bashforth numerical scheme is used to solve the system of equations. Stability conditions are presented in details. To corroborate the analytical results, an example is given with numerical simulation. Mathematics Subject Classification [2010]: 26A33, 35B35, 65D25, 65L20.

Solving a Fractional-Order Differential Equation Using Rational Symmetric Contraction Mappings

The intent of this manuscript is to present new rational symmetric ϖ−ξ-contractions and infer some fixed-points for such contractions in the setting of Θ-metric spaces. Furthermore, some related results such as Suzuki-type rational symmetric contractions, orbitally Υ-complete, and orbitally continuous mappings in Θ-metric spaces are introduced. Ultimately, the theoretical results are shared to study the existence of the solution to a fractional-order differential equation with one boundary stipulation.

Fractional differential equation with uncertainty

We consider a fractional order differential equation with uncertainty and introduce the concept of solution. It goes beyond ordinary first-order differential equations and differential equations with uncertainty.

Improvement of Mathematical Model for Sedimentation Process

In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers the Basset force’s fractional origin and contains the Riemann–Liouville fractional integral rewritten as a Grunwald–Letnikov derivative. As a result, the general solution of the proposed fractional-order differential equation was found analytically. The belonging of this solution to the real range of values was strictly theoretically proven. The obtained solution was validated on a particular analytical case study. In addition, it was proven numerically with the approach based on the S-approximation method using the block-pulse operational matrix. The proposed mathematical model can be applied for modeling the processes of fine particles sedimentation in liquids, aerosol deposition in gas flows, and particle deposition in gas-dispersed systems.

Solution of Fractional Differential Equations Utilizing Symmetric Contraction

The aim of this paper is to present another family of fractional symmetric α - η -contractions and build up some new results for such contraction in the context of ℱ -metric space. The author derives some results for Suzuki-type contractions and orbitally T -complete and orbitally continuous mappings in ℱ -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in ℱ -metric space.