Abstract
Based on an equivalent integral equation of a new type for a class of fractional evolution equations, which is different from those obtained in the existing literature, the paper investigates a class of fractional evolution equations with nonlocal conditions on infinite interval. Without the assumption of lower and upper solutions, we present a new result on the existence and uniqueness of positive mild solutions for the abstract fractional evolution equations by using the monotone iterative method.
Highlights
Fractional calculus, a generalization of the ordinary differentiation and integration, has played a significant role in science, economy, engineering, biology, physics, and other fields
Many real world phenomena and processes can be modeled as fractional differential equations, and due to the fact of their various applications in many fields, today, there is a large number of researchers turning to study the fractional differential equations
Among most of the studies on fractional differential equations, an important branch is devoted to investigating the fractional evolution equation, which is a valuable tool for describing physics phenomena
Summary
Fractional calculus, a generalization of the ordinary differentiation and integration, has played a significant role in science, economy, engineering, biology, physics, and other fields (see [ – ]). For more general theory of fractional differential equations, we refer readers to the papers [ – ] and the references given therein. In [ ], EI-Borai investigated the Cauchy problem in a Banach space for fractional evolution equations.
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