Analysis of a Fractional-Order Quadratic Functional Integro-Differential Equation with Nonlocal Fractional-Order Integro-Differential Condition

Abstract

Here, we center on the solvability of a fractional-order quadratic functional integro-differential equation with a nonlocal fractional-order integro-differential condition in the class of continuous functions. The maximal and minimal solutions will be discussed. The continuous dependence of the solutions on a few parameters will be examined. Finally, the problems of conjugate orders and integer orders, and some other problems and remarks will be discussed and presented.

Keywords

• Caputo fractional derivative
• fractional-order integro-differential equations
• conjugate-order integro-differential equations
• Schauder fixed-point theorem
• maximal and minimal solutions
• continuous dependence