Controllability of a Class of Impulsive ψ-Caputo Fractional Evolution Equations of Sobolev Type

Controllability of Impulsive Fractional Evolution Integrodifferential Equations in Banach Spaces

According to fractional calculus theory and Banach’s fixed point theorem, we establish the sufficient conditions for the controllability of impulsive fractional evolution integrodifferential equations in Banach spaces. An example is provided to illustrate the theory.

Stability of Solutions to Impulsive Caputo Fractional Differential Equations

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several suffic...

Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces

and Applied Analysis 3 To investigate the approximate controllability of system (9), we assume the following conditions. (H4) The functionf:[0, b]×X → X satisfies the following: (a) f(t, ⋅) : X → X is continuous for each t ∈ [0, b] and for each x ∈ X, f(⋅, x) : [0, b] → X is strongly measurable; (b) there is a positive integrable function n ∈ L 1 ([0, b], [0, +∞)) and a continuous nondecreasing...

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

the investigation of the relationship between type a and type b personalities and quality of translation

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