How the fractional operators are defined? It might be summarized as follows: “each fractional operator is the action of a particular special function on a general function, which usually represents the solution of a well-defined problem by using a suitable integral transform.” See for example. One attractive aspect of this approach is to model complex systems by taking into account the effects of filtration and memory. Use of fractional operators has become a remarkable tool to study new technology and researches. Similar properties of existing distributions can be deduced. Furthermore, the new function is used to generate a probability density function, and its statistical properties are explored. Hence, the results are also validated with the earlier obtained results for gamma function as special cases. Properties of this modified function are discussed by investigating a new series representation involving delta function. Present motivation is to define a new special function by modification in the original gamma function with Mittag-Leffler function. Recent applications of Mittag-Leffler function have reshaped the scientific literature due to its fractional effects that cannot be obtained by using exponential function. Mittag-Leffler function is a natural generalization of the exponential function.
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