Applications of fractional calculus to parabolic starlike and uniformly convex functions

By Hari M. Srivastava, A. K. Mishra. 2000

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On classes of analytic functions related to conic domains (2008, result): “SPα,0(1,0)≡ SPα (Srivastava and Mishra [25]); 9.”
CERTAIN SUFFICIENCY CONDITIONS ON GAUSSIAN HYPERGEOMETRIC FUNCTIONS (2004, methodology): “The classes UCV and Sp are unified and studied using certain fractional calculus operator methods found in [ 18 ].”
Hypergeometric functions in the parabolic starlike and uniformly convex domains (2007, methodology): “The various properties of the function classes k-UCV and k-ST were investigated extensively by Kanas and Srivastava [7] and by Srivastava and Mishra [8].”
Stability and existence results for a class of nonlinear fractional differential equations with singularity (2018, background): “Green function β(t, s) given by (4) satisfies the next properties: (1)β(t, s) > 0 for all 0 < s, t < 1; (2)β(t, s) is nondecreasing function and maxt∈(0,1)β(t, s) = β(1, s); (3)tβ−1maxt∈(0,1)β(t, s) ≤ β(t, s) for 0 < s, t < 1.”