scholarly journals On the use of Mellin transform to a class of q-difference-differential equations

2000 ◽  
Vol 268 (4-6) ◽  
pp. 217-223 ◽  
Author(s):  
Choon-Lin Ho
Keyword(s):  
Differential Equations ◽  
Mellin Transform

Hyers-Ulam stability of Hermite fuzzy differential equations and fuzzy Mellin transform

2018 ◽  
Vol 35 (3) ◽  
pp. 3721-3731 ◽  
Author(s):  
Wenjuan Ren ◽  
Zhanpeng Yang ◽  
Xian Sun ◽  
Min Qi
Keyword(s):  
Differential Equations ◽  
Mellin Transform ◽  
Ulam Stability

scholarly journals On Solvability Conditions for a Certain Conjugation Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 234
Author(s):  
Vladimir Vasilyev ◽  
Nikolai Eberlein
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Mellin Transform ◽  
Algebraic Equations ◽  
Conjugation Problem ◽  
Solvability Conditions ◽  
Linear Algebraic Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.

scholarly journals Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

2013 ◽  
Vol 25 (1) ◽  
pp. 27-43 ◽  
Author(s):  
MARIANITO R. RODRIGO
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Boundary Layers ◽  
Mellin Transform ◽  
Call Option ◽  
Option Prices ◽  
Analytical Formulas ◽  
American Put

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.

Derivation of Green-type, transitional, and uniform asymptotic expansions from differential equations II. Whittaker functions W k,m for large k , and for large | K 2 – m 2 |

1964 ◽  
Vol 281 (1384) ◽  
pp. 111-129 ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Whittaker Functions ◽  
Transform Method ◽  
Special Cases ◽  
Uniform Expansions ◽  
Uniform Asymptotic Expansions

The method for deriving Green-type asymptotic expansions from differential equations, introduced in I and illustrated therein by detailed calculations on modified Bessel functions, is applied to Whittaker functions W k,m , first for large k , and then for large |k 2 —m 2 |. Following the general theory of I, combination of this procedure with the Mellin transform method yields asymptotic expansions valid in transitional regions, and general uniform expansions. Weber parabolic cylinder and Poiseuille functions are examined as important special cases.

scholarly journals A Method for Solving Initial and Boundary Value Fuzzy differential equations by Mellin Transform

2021 ◽  
Author(s):  
Noreen Azhar ◽  
Saleem Iqbal
Keyword(s):  
Differential Equations ◽  
Mellin Transform ◽  
Boundary Value ◽  
Transform Method ◽  
Generalized Differentiability ◽  
Strongly Generalized Differentiability

Abstract This Paper is included fuzzy concepts of Mellin transform along with its operational properties. Mellin transform method is applicable in fuzzy context. The study involved the proposed techniques for solving initial and boundary value fuzzy differential equations under strongly generalized differentiability concepts.

On Solving Certain Fractional Differential Equations With Right-Sided Derivatives

2009 ◽  
Author(s):  
Malgorzata Klimek
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Mellin Transform ◽  
Transform Method ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Meijer G Function ◽  
The Right ◽  
Derivatives Of

In the paper, solutions of basic fractional differential equations with right-sided derivatives of order α and with variable tβ - potential are derived using the Mellin transform method. The results are Meijer G-function series fulfilling the respective boundary conditions. The obtained series are transformed into solutions of analogous equations with left-sided derivatives and (b – t)β - potential. As an example case α + β = α/J is studied and for J = 1 the eigenfunctions of the right-sided Riemann-Liouville derivative are recovered.

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