New exploration of operators of fractional neutral integro-differential equations in Banach spaces through the application of the topological degree concept

Abstract

<abstract><p>In this paper, we analyze the behavior of the neutral integro-differential equations of fractional order including the Caputo-Hadamard fractional derivative. The results and solutions are obtained using the topological degree method. Furthermore, some specific numerical examples are given to ascertain the wide applicability and high efficiency of the suggested fixed point technique.</p></abstract>

Novel Exploration of Topological Degree Method for Non-Instantaneous Impulsive Fractional Integro-Differential Equation through Application of Filtering System

“…Remark 3.7 One can observe that the above existence and uniqueness results (see theorems (3.5) and (3.6)) are based on the Ξ− Lipschitz, Ξ− condensing, TDM and Grownwall's inequality. This method is help to prove our result using weaker conditions instead of stronger conditions [3], [4], [8], [9], and [21]. The assumptions (P1)(ii) and (P2)(ii) are satisfied the equation ( 13) then by using the theorems (3.3) and (3.5), we can say the equation ( 13) has a solution on C(ℑ, R n ).…”

“…• These assumptions and applications have never been employed before in any research articles and it will be yield a more effective result than prior studies ( [9], [10], [13], [15], [18], [19], [23], and [24]).…”

An effective analytical method for fractional Brusselator reaction–diffusion system

“…Compared to the integer order calculus, it has a greater degree of freedom. Many of its characteristics do not exist in integer order calculus, which fascinates many young researchers to contribute more to fractional calculus [6][7][8][9][10][11][12][13][14][15]. In recent years, there have been a pile of research articles about the analytical and numerical solution of fractional calculus by various methods.…”

Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces

“…with A 2 and A 3 n × n matrices whose elements belong to L 2 (−1, 0); B is a constant n × r matrix; and the control u is an L 2 -function [1]. Nowadays, many researchers have investigated neutral differential equations in Banach spaces [2][3][4]. This interest is explained by the fact that neutral-argument differential equations have interesting applications in real-life problems: they appear, e.g., while modeling networks containing lossless transmission lines or in super-computers.…”