On Laplace transforms with respect to functions and their applications to fractional differential equations

DOI10.1002/mma.7772arXiv1907.04541OpenAlexW3201196590MaRDI QIDQ6140808

Mujeeb Ur Rehman, Hafiz Muhammad Fahad, Arran Fernandez

Publication date: 2 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.04541

zbMATH Keywords

Laplace transformfractional calculusfractional differential equations\(\Psi\)-fractional calculusgeneralised fractional operators

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Fractional derivatives and integrals (26A33) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Laplace transform (44A10) Fractional ordinary differential equations (34A08)

Related Items (5)

A note on function space and boundedness of the general fractional integral in continuous time random walk ⋮ Approximate solution of GCF PDM Schrödinger equation for a symmetrical modified Pöschl-Teller potential by GCF Laplace transform method ⋮ Stability and \(\psi\)-algebraic decay of the solution to \(\psi\)-fractional differential system ⋮ On the fractional Fourier transforms with respect to functions and its applications ⋮ Unified predictor-corrector method for fractional differential equations with general kernel functions

Cites Work

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• New approach to a generalized fractional integral
• Laplace transform and fractional differential equations
• On Caputo modification of the Hadamard fractional derivatives
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Namias' fractional Fourier transforms on \(L^ 2\) and applications to differential equations
• Operational calculus
• The fractional Dodson diffusion equation: a new approach
• A note on Hadamard fractional differential equations with varying coefficients and their applications in probability
• A Caputo fractional derivative of a function with respect to another function
• Solving PDEs of fractional order using the unified transform method
• On fractional calculus with general analytic kernels
• Generalized substantial fractional operators and well-posedness of Cauchy problem
• Tempered and Hadamard-type fractional calculus with respect to functions
• The Prabhakar or three parameter Mittag-Leffler function: theory and application
• On the \(\psi\)-Hilfer fractional derivative
• Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions
• One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Generalized mittag-leffler function and generalized fractional calculus operators
• A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator
• A class of fractional integral transforms: a generalization of the fractional Fourier transform
• An Integral Equation Involving Legendre Functions
• The Fractional Derivative of a Composite Function

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