New identities for the Wright and the Mittag-Leffler functions using the Laplace transform

DOI10.1142/S1793557114500387zbMath1302.33019MaRDI QIDQ2925275

Alireza Ansari, Amirhossein Refahi Sheikhani

Publication date: 21 October 2014

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Laplace transformStieltjes transformMittag-Leffler functionWright function

Mathematics Subject Classification ID

Mittag-Leffler functions and generalizations (33E12) Laplace transform (44A10)

Related Items (13)

Numerical scheme to solve a class of variable-order Hilfer-Prabhakar fractional differential equations with Jacobi wavelets polynomials ⋮ Analytical studies for linear periodic systems of fractional order ⋮ Logarithmic functions are eigenfunctions of integral operators with \(M\)-Wright kernels ⋮ Wiener-Hopf technique for a fractional mixed boundary value problem in cylindrical layer ⋮ A new three-dimensional chaotic system: dynamical properties and simulation ⋮ Solution of the space-fractional Benjamin-Ono equation: an operational approach ⋮ On M-Wright transforms and time-fractional diffusion equations ⋮ A Collocation Method for Solving Fractional Order Linear System ⋮ On Hyers-Ulam stability of fractional differential equations with Prabhakar derivatives ⋮ Stability analysis of distributed-order Hilfer-Prabhakar systems based on inertia theory ⋮ Asymptotic analysis of the Wright function with a large parameter ⋮ Unnamed Item ⋮ Some results involving integral transforms of Airy functions

Cites Work

• Identities for the exponential integral and the complementary error transforms
• A theorem on the generalized Stieltjes transform and its applications
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The Wright functions as solutions of the time-fractional diffusion equation.
• Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus
• The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation
• New method for solving system of P.F.D.E. and fractional evolution disturbance equation of distributed order
• SOLUTION TO SYSTEM OF PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS USING THE $\mathcal{L}_2$-TRANSFORM

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