Laplace transform for solving some families of fractional differential equations and its applications

DOI10.1186/1687-1847-2013-137zbMath1390.34025OpenAlexW2110908069WikidataQ59300417 ScholiaQ59300417MaRDI QIDQ1648707

Shy-Der Lin, Chia-Hung Lu

Publication date: 27 June 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-137

zbMATH Keywords

gamma functionMittag-Leffler functionWright functionRiemann-Liouville fractional integralsfractional-order differential equationsLaplace transform of the fractional derivative

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Fractional ordinary differential equations (34A08)

Related Items (24)

A new and elegant approach for solving \(n\times n\)-order linear fractional differential equations ⋮ On the reasonability of linearized approximation and Hopf bifurcation control for a fractional-order delay Bhalekar-Gejji chaotic system ⋮ Solution of fractional partial differential equations using fractional power series method ⋮ Stability and Hopf bifurcation analysis of fractional-order complex-valued neural networks with time delays ⋮ A Degenerate Parabolic Logistic Equation ⋮ Numerical calculations accuracy comparison of the inverse Laplace transform algorithms for solutions of fractional order differential equations ⋮ Discrete waveform relaxation method for linear fractional delay differential-algebraic equations ⋮ Integral representation of solutions of fractional system with distributed delays ⋮ Analysis of \(( \alpha, \beta )\)-order coupled implicit Caputo fractional differential equations using topological degree method ⋮ Generalized fractional power series solutions for fractional differential equations ⋮ The Atiyah-Singer index theorem for a family of fractional Dirac operators on spin geometry ⋮ The asymptotic solutions of two-term linear fractional differential equations via Laplace transform ⋮ Unnamed Item ⋮ The analysis of fractional-order Navier-Stokes model arising in the unsteady flow of a viscous fluid via Shehu transform ⋮ Regional controllability analysis of fractional diffusion equations with Riemann-Liouville time fractional derivatives ⋮ Fractional Laplace transform method in the framework of the CTIT transformation ⋮ Unnamed Item ⋮ The new semianalytical technique for the solution of fractional-order Navier-Stokes equation ⋮ Theorems on some families of fractional differential equations and their applications. ⋮ Stability analysis of a fractional-order SEIR-KS computer virus-spreading model with two delays ⋮ Determination of order in linear fractional differential equations ⋮ Chaos, Hopf bifurcation and control of a fractional-order delay financial system ⋮ On the stability and convergence of difference schemes for the generalized fractional diffusion equation with Robin boundary value conditions ⋮ Approximate Solutions to Fractional Boundary Value Problems by Wavelet Decomposition Methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A class of extended fractional derivative operators and associated generating relations involving hypergeometric functions
• The fundamental solutions for the fractional diffusion-wave equation
• Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions
• Some families of series identities and associated fractional differintegral formulas

This page was built for publication: Laplace transform for solving some families of fractional differential equations and its applications