Analysis of a hybrid integro-differential inclusion

Abstract

Our main objectives in this paper are to investigate the existence of the solutions for an integro-differential inclusion of second order with hybrid nonlocal boundary value conditions. The sufficient condition for the uniqueness of the solution will be given and the continuous dependence of the solution on the set of selections and on other functions will be proved. As an application, the nonlocal problem of the Chandrasekhar hybrid second-order functional integrodifferential inclusion and some particular cases will be presented. Also, we provide some examples to illustrate our results.

An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control

“…Many scholars have discussed mathematical models for thermostats, for example, refs. [1][2][3][4][5][6][7][8][9][10].…”

“…Hybrid differential equations have received great attention [1,9,14,15]. Dhage and Lakshmikantham [14] initiated and presented a discussion of hybrid differential equations.…”

“…Recently, the authors of [9] have established a model for thermostats involving hybrid integro-differential inclusions:…”

“…Inspired by the investigated mathematical models in [9,11], we establish some existence results for hybrid fractional modeling of thermostats.…”

Existence and Hyers-Ulam stability of solutions to the implicit second-order differential equation via fractional integral boundary conditions

“…There has been a huge advancement in fractional derivatives with Riemann-Liouville, Caputo, Hilfer, Hadamard, and others. Ongoing outcomes on fractional calculus and fractional differential equations can be found in [7,[17][18][19][20]29]. The Caputo fractional derivative has recently been applied in different areas of the physical interpretation of initial conditionsand boundary conditions.…”