Operational calculus for the Riemann-Liouville fractional derivative with respect to a function and its applications

DOI10.1515/fca-2021-0023zbMath1498.26010OpenAlexW3162340984WikidataQ114053063 ScholiaQ114053063MaRDI QIDQ2046073

Arran Fernandez, Hafiz Muhammad Fahad

Publication date: 17 August 2021

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/fca-2021-0023

zbMATH Keywords

fractional differential equationsoperational calculusMikusiński operational calculusfractional calculus with respect to functions

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Calculus of Mikusi?ski and other operational calculi (44A40) Classical operational calculus (44A45)

Related Items (13)

Solving Prabhakar differential equations using Mikusiński's operational calculus ⋮ On a variant of multivariate Mittag-Leffler's function arising in the Laplace transform method ⋮ Mikusiński's operational calculus for Prabhakar fractional calculus ⋮ On the importance of conjugation relations in fractional calculus ⋮ A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions ⋮ Generalising the fractional calculus with Sonine kernels via conjugations ⋮ Incommensurate multi‐term fractional differential equations with variable coefficients with respect to functions ⋮ Mikusiński's operational calculus for general conjugated fractional derivatives ⋮ Abstract algebraic construction in fractional calculus: parametrised families with semigroup properties ⋮ An operational calculus formulation of fractional calculus with general analytic kernels ⋮ Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations ⋮ On fractional calculus with analytic kernels with respect to functions ⋮ Unified predictor-corrector method for fractional differential equations with general kernel functions

Cites Work

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• On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives
• An operational method for solving fractional differential equations with the Caputo derivatives
• The exact solution of certain differential equations of fractional order by using operational calculus
• Solving PDEs of fractional order using the unified transform method
• Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives
• A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators
• A new collection of real world applications of fractional calculus in science and engineering
• Explicit solutions for linear variable-coefficient fractional differential equations with respect to functions
• A numerical study of fractional relaxation-oscillation equations involving \(\psi \)-Caputo fractional derivative
• Historical survey: the chronicles of fractional calculus
• Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations
• Multivariate analogue of generalized Mittag-Leffler function
• Operationl method for solving generalized abel integral equation of second kind
• A generalisation of the Malgrange–Ehrenpreis theorem to find fundamental solutions to fractional PDEs
• Mittag-Leffler Functions, Related Topics and Applications
• Oscillatory solutions of fractional integro‐differential equations
• Operational calculus for the Caputo-type fractional Erdélyi–Kober derivative and its applications
• Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series

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