An Iterative Scheme for a Class of Fractional Order Perturbed Differential Equations

Roy, Rajarshi; Kumar, K. Harish

doi:10.1007/978-981-13-9939-8_14

Cited by 1 publication

(1 citation statement)

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“…In recent years, there are several contributions focusing on fractional differential equations, mainly on the existence, uniqueness, and stability of solutions. For more details, the readers are referred to the previous studies [4,5,6,7,9,15,17,18,19,20,21,22,23,24,35,36,41,43,49,50,51,52,53,54,55] and the references therein. The main techniques used in these studies are fixed-point techniques, Leray-Schauder theory, coincidence theory, or monotone iterative technique combined with the method of upper and lower solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness, approximation of solutions and Ealpha-Ulam stability results for a class of nonlinear fractional differential equations involving psi-Caputo derivative with initial conditions

Derbazi¹,

Baitiche²,

Benchohra³

et al. 2021

Mathematica Moravica

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The main purpose of this paper is to study the existence, uniqueness, Ea-Ulam stability results, and other properties of solutions for certain classes of nonlinear fractional differential equations involving the ps-Caputo derivative with initial conditions. Modern tools of functional analysis are applied to obtain the main results. More precisely using Weissinger's fixed point theorem and Schaefer's fixed point theorem the existence and uniqueness results of solutions are proven in the bounded domain. While the well known Banach fixed point theorem coupled with Bielecki type norm are used with the end goal to establish sufficient conditions for existence and uniqueness results on unbounded domains. Meanwhile, the monotone iterative technique combined with the method of upper and lower solutions is used to prove the existence and uniqueness of extremal solutions. Furthermore, by means of new generalizations of Gronwall's inequality, different kinds of Ea-Ulam stability of the proposed problem are studied. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility and correctness of the main results.

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