One of the tools for building new fixed-point results is use symmetry in distance functions. The symmetric property metrics particularly useful constructing contractive inequalities analyzing different models practical consequences. A lot important invariant point crisp mappings have been improved by using metrics. However, more than a handful theorems spaces are yet to be investigated fuzzy ve...

In this work we study integral boundary value problem involving Caputo differentiation  cD tu(t) = f(t, u(t)), 0 < t < 1, αu(0)− βu(1) = ∫ 1 0 h(t)u(t)dt, γu′(0)− δu′(1) = ∫ 1 0 g(t)u(t)dt, where α, β, γ, δ are constants with α > β > 0, γ > δ > 0, f ∈ C([0, 1]×R+,R), g, h ∈ C([0, 1],R+) and cD t is the standard Caputo fractional derivative of fractional order q(1 < q < 2). By using some fix...

*Correspondence: [email protected] Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Chang’an Road, Xi’an, China Abstract In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative. The new kernel of Capu...

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classical theory of linear viscoelasticity, we contrast these two types of fractional derivatives in thei...

We consider probability mass functions V supported on the positive integers using arguments introduced by Caputo, Dai Pra and Posta, based on a Bakry–Émery condition for a Markov birth and death operator with invariant measure V . Under this condition, we prove a new modified logarithmic Sobolev inequality, generalizing and strengthening results of Wu, Bobkov and Ledoux, and Caputo, Dai Pra and...

Many dynamic systems can be modeled by fractional differential equations in which some external parameters occur under uncertainty. Although these increase the complexity, they present more acceptable solutions. With aid of Atangana-Baleanu-Caputo (ABC) operator, an advanced numerical-analysis approach is considered and applied this work to deal with different classes fuzzy integrodifferential ...

This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some exi...

The fuzzy fractional differential equation explains more complex real-world phenomena than the does. Therefore, numerous techniques have been timely derived to solve various time-dependent models. In this paper, we develop two compact finite difference schemes and employ resulting obtain a certain solution for time-fractional convection–diffusion equation. Then, by making use of Caputo derivati...