Existence and Uniqueness of Positive Solutions for a Fractional Switched System

Abstract

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: ( 0+ ( )+ ( ) ( , ( ))+ ( ) ( , ( )) = 0, ∈ = [0, 1]); ( (0) = (0) = 0, (1) = ∫ 1 0 ( ) ), where 0+ is the Caputo fractional derivative with 2 < ≤ 3, ( ) : → {1, 2, . . . , } is a piecewise constant function depending on , and R + = [0, +∞), , ∈ [ × R + , R + ], = 1, 2, . . . , . Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results. 1 0 ( ) ,

Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

“…As of late, it has been demonstrated that the differential designs including derivatives of fractional order emerge in numerous technological innovations and scientific disciplines as the statistical modeling of frameworks and procedures in numerous fields-case in point: physical science, chemical industry, aerodynamics, electrodynamics of complex medium, etc. For information, such as some uses and latest outcomes, think about the treatise of Abbas et al [1], Baleanu et al [2], Podlubny [3], Diethelm [4], Kilbas et al [5], and Tarasov [6], and the papers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and the references cited therein.…”

Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

“…We can locate the various uses of FDE in control theory, nonlinear oscillation of earthquake, the fluid-dynamic traffic model, aerodynamics and in nearly every discipline of science and engineering. For fundamental certainties about fractional systems, one can make reference to the books [1,2], and the papers [3,4,5,6,7,8,9], and the references cited therein. FDE with delay features happen in several areas such as medical and physical with SDD or non-constant delay.…”

Existence and Controllability of Fractional Neutral Integro-Differential Systems With State-Dependent Delay in Banach Spaces

“…These days, it has been shown that the differential models including derivatives of fractional order occur in lots of engineering and scientific professions as the mathematical modeling of systems and strategies in numerous domains, for case in point, basic sciences, navigation, feed back amplifiers, and neuron modelling so on. For crucial confirmations about fractional frameworks, one can make reference to the treatises [1,2], and the papers [3][4][5][6][7][8][9], and the references cited therein. FDE with delay characteristics happen in a number of domains such as medical and physical with SDD or non-constant delay.…”