Existence and data dependence results for neutral fractional order integro-differential equations

Abstract

<abstract><p>We assess the multi-derivative nonlinear neutral fractional order integro-differential equations with Atangana-Baleanu fractional derivative of the Riemann-Liouville sense. We discuss results about the existence and difference solution on some data, based on the Prabhakar fractional integral operator $ \varepsilon^{\alpha}_{\delta, \eta, \mathcal{V}; c+} $ with generalized Mittag-Leffler function. The results are obtained by using Krasnoselskii's fixed point theorem and the Gronwall-Bellman inequality.</p></abstract>

New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

“…In further works we will extend the applicability of the combined method of the Modified Atangana-Baleanu fractional derivative and the MHPM to solve other complex phenomena like those described by the fractional Fisher equation, the fractional diffusion equation, the fractional Klein-Gordon equation and other important fractional equations relevant in physics, engineering, and other areas like those discussed previously in the [28][29][30][31][32][33][34][35][36][37][38][39]. In all these research that involves fractional derivatives with non singular fractional to fulfill the Figure 3.…”

“…The Covid-19 infection spread have been studied by introducing fractional model with the help of Caputo-Fabrizio and Atangana-Baleanu derivative in the Caputo sense [37], also the Atangana-Baleanu derivative has been considered for the analysis of Lévy noise driven Hepatitis B virus (HBV) infectious disease by considering the vaccination effect on its dynamical behavior [38]. Other important fields that recently have attract the attention of several researchers is the modeling of different systems by mixing different fractional derivatives, like the Caputo derivative with the Atangana-Baleanu and other fractional derivatives in the same model, see for example [39].…”

A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

“…Many academics have recently considered the exact and approximate controllability of *Corresponding Author systems characterized by impulsive functional inclusions, integro-differential equations, semilinear functional equations, neutral functional differential equations, and evolution inclusions, to name a few examples, see [23,24,27] and references in that. In [28][29][30][31][32][33][34] Ravi et. al.…”

Results on fractional integrodifferential equations with fractional boundary conditions by using a special type of operators over general Banach spaces with bounded approximation numbers

“…In [22][23][24], the authors proposed a new explicit numerical scheme based on two-step Lagrange polynomial for solving nonlinear FDEs of AB derivative and also presented the error analysis. [18,34,35] has defined higherorder AB fractional operators and established some useful relations among the operators. Some recent progress on the existence of solutions to various higher-order nonlinear FDEs based on AB derivative with classical boundary conditions can be found in a series of papers.…”