Abstract
This paper presents the Sumudu transform method and its hybrid for the construction of solutions of differential equations, both with integer-order and fractional derivatives. The paper discusses the construction of solutions of fractional differential equations with varying delay proportional to the independent variable by using two methods. The paper considers the mathematical model for the decay of Iodine 135 as an application of fractional differential equations in nuclear physics. The application indicates that fractional differential equations with variable delay proportional to the independent variable are a useful tool for the modeling of many anomalous phenomena in nature and in the theory of complex systems.
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