An operational calculus formulation of fractional calculus with general analytic kernels

DOI10.3934/era.2022216OpenAlexW4312714491MaRDI QIDQ2699102

Arran Fernandez, Noosheza Rani

Publication date: 26 April 2023

Published in: Electronic Research Archive (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/era.2022216

zbMATH Keywords

fractional derivativesMikusiński's operational calculusfractional differential equationsfractional integralsoperational calculus

Mathematics Subject Classification ID

Real functions (26-XX) Partial differential equations (35-XX)

Cites Work

• General fractional calculus, evolution equations, and renewal processes
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• An operational method for solving fractional differential equations with the Caputo derivatives
• Representations of acting processes and memory effects: general fractional derivative and its application to theory of heat conduction with finite wave speeds
• On fractional calculus with general analytic kernels
• Operational calculus for the general fractional derivative and its applications
• Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications
• Solving Prabhakar differential equations using Mikusiński's operational calculus
• Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
• A new collection of real world applications of fractional calculus in science and engineering
• Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations
• A derivative concept with respect to an arbitrary kernel and applications to fractional calculus
• Mikusiński's operational calculus for Prabhakar fractional calculus
• An Operational Method in Partial Differential Equations
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