Abstract
In this paper, we discuss the existence and uniqueness of mild and classical solutions of quasilinear mixed integrodifferential equations of frac- tional orders with nonlocal condition in Banach spaces. Furthermore, we study continuous dependence of mild solutions. Our analysis is based on fractional calculus, resolvent operators and Banach's fixed point theorem.
Highlights
In recent years a considerable interest has been shown in the so-called fractional calculus, which allows us to consider integration and differentiation of any order, not necessarily integer
One of the emerging branches of this study is the theory of fractional quasilinear equations, i.e. quasilinear equations where the integer derivative with respect to time is replaced by a derivative of fractional order
Much attention has been paid to existence results for the nonlinear mixed integrodifferential equations with nonlocal condition in Banach spaces, see Dhakne et al [20]
Summary
In recent years a considerable interest has been shown in the so-called fractional calculus, which allows us to consider integration and differentiation of any order, not necessarily integer. The existence of solutions of fractional abstract differential equations with nonlocal initial condition was investigated by [30]. Much attention has been paid to existence results for the nonlinear mixed integrodifferential equations with nonlocal condition in Banach spaces, see Dhakne et al [20]. Several authors have studied the existence of solutions of abstract nonlocal problems by using different techniques, see [3, 12, 21, 25, 26, 36, 37] and the references given therein. Existence and uniqueness; mild and classical solutions; fractional integrodifferential equation; resolvent operators; Banach’s fixed point theorem; nonlocal condition. The main tool employed in our analysis is based on the Banach fixed point theorem, resolvent operators and fractional calculus.
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