A note on Hadamard fractional differential equations with varying coefficients and their applications in probability
TLDR
In this paper, the authors show connections between special functions arising from generalized COM-Poisson type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators.Abstract:
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results are obtained, showing the particular role of Hadamard-type derivatives in connection with a recently introduced generalization of the Le Roy function. We are also able to prove a general connection between fractional hyper-Bessel-type equations involving Hadamard operators and Le Roy functions.read more
Citations
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Short memory fractional differential equations for new memristor and neural network design
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Fractional Calculus: Theory and Applications
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A Guide to Special Functions in Fractional Calculus
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Study on Krasnoselskii’s fixed point theorem for Caputo–Fabrizio fractional differential equations
TL;DR: In this article, the existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative is established by using usual classical fixed point theorems of Banach and Krasnoselskii.
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Utilizing fixed point approach to investigate piecewise equations with non-singular type derivative
TL;DR: In this paper , the authors derived necessary results for the existence, uniqueness and various form of Hyers-Ulam (H-U) type stability for the considered problem, using classical fixed point theorems due to Banach and Krasnoselskii's.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
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Generalized fractional calculus and applications
TL;DR: In this paper, generalized operators of fractional integration and differentiation have been applied to generalized hypergeometric functions and their applications have been discussed. But they are not suitable for the special functions used in this paper.
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Mittag-Leffler Functions, Related Topics and Applications
TL;DR: In this article, the authors present a self-contained, comprehensive treatment of the theory of the Mittag-Leffler functions, ranging from rather elementary matters to the latest research results, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena.