| Summary: | In the present paper, a new operator denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>z</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msubsup><msubsup><mi>L</mi><mrow><mi>α</mi></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula> is defined by using the fractional integral of Sălăgean and Ruscheweyh operators. By means of the newly obtained operator, the subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mfenced separators="" open="(" close=")"><mi>δ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>λ</mi></mfenced></mrow></semantics></math></inline-formula> of analytic functions in the unit disc is introduced, and various properties and characteristics of this class are derived by applying techniques specific to the differential subordination concept. By studying the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>z</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msubsup><msubsup><mi>L</mi><mrow><mi>α</mi></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula>, some interesting differential subordinations are also given.
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