On (<i>p</i>,<i>q</i>)-Analogues of Laplace-Typed Integral Transforms and Applications

• Main Authors: Sansumpan Jirakulchaiwong, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas, Hwajoon Kim
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Symmetry
• Subjects: (<i>p,q</i>)-laplace-typed integral transforms; (<i>p,q</i>)-derivative; (<i>p,q</i>)-integral; (<i>p,q</i>)-calculus; (<i>p,q</i>)-difference equations; (<i>p,q</i>)-convolution theorem
• Online Access: https://www.mdpi.com/2073-8994/13/4/631

In this paper, we establish <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogues of Laplace-type integral transforms by using the concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-calculus. Moreover, we study some properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-analogues of Laplace-type integral transforms and apply them to solve some (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></semantics></math></inline-formula>)-differential equations.