Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach

Abstract

In this article, we establish the existence of solutions for a functional integral equation of fractional order. The study upholds the case when the set-valued function has L 1-Carathèodory selections, we reformulate the functional integral inclusion according to these selections via a classical fixed point theorem of Schauder and present theorem for the existence of integrable solutions. As an application, the existence of solutions of nonlinear functional integro-differential inclusion with an initial value, and the initial value problem for the arbitrary-order differential inclusion will be studied.

Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

“…Using the fixed point technique (Alternative theorem), we study HUR stability of the φ-Hadamard fractional Volterra integro-differential equation (23) in MVFB-space (W, S , ). Our results can apply to improve recent results [17] and by methods used in this paper we can extend some fractional Volterra integro-differential equations in MVFBspaces [18][19][20].…”

Radu–Miheţ Method for the Existence, Uniqueness, and Approximation of the ψ-Hilfer Fractional Equations by Matrix-Valued Fuzzy Controllers

“…Our results can be applied to improve recent results [5], and by the methods used in this paper, we can extend some fractional Volterra integro-differential equations in MVF-k-Bspaces [11][12][13][14].…”

The Cădariu-Radu Method for Existence, Uniqueness and Gauss Hypergeometric Stability of Ω-Hilfer Fractional Differential Equations

“…In this section, as an application, we apply our main result to prove an example. Our main result can be applied for recent results presented in [25][26][27][28][29][30][31][32][33][34][35]. Example 1.…”