The Laplace transform induced by the deformed exponential function of two variables
-
Predrag M. Rajković
,
Miomir S. Stanković
Abstract
Based on the easy computation of the direct transform and its inversion, the Laplace transform was used as an effective method for solving differential and integral equations. Its various generalizations appeared in order to be used for treating some new problems. They were based on the generalizations and deformations of the kernel function and of the notion of integral. Here, we expose our generalization of the Laplace transform based on the so-called deformed exponential function of two variables. We point out on some of its properties which hold on in the same or similar manner as in the case of the classical Laplace transform. Relations to a generalized Mittag-Leffler function and to a kind of fractional Riemann-Liouville type integral and derivative are exhibited.
Acknowledgements
This paper is supported by the Ministry of Science and Technological Development of the Republic Serbia, Projects No 174011 and No 44006.
It is related also to the working program on a bilateral agreement between Serbian Academy of Sciences and Arts and Bulgarian Academy of Sciences, 2017–2019.
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© 2018 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 21–3–2018)
- Research Paper
- Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces
- Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance
- The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces
- Parallel algorithms for modelling two-dimensional non-equilibrium salt transfer processes on the base of fractional derivative model
- Some iterated fractional q-integrals and their applications
- Lebesgue regularity for nonlocal time-discrete equations with delays
- Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions
- Error estimates of high-order numerical methods for solving time fractional partial differential equations
- The Laplace transform induced by the deformed exponential function of two variables
- Attractivity for fractional evolution equations with almost sectorial operators
- The multiplicity solutions for nonlinear fractional differential equations of Riemann-Liouville type
- Well-posedness of general Caputo-type fractional differential equations
- Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions
- Inverse source problem for a space-time fractional diffusion equation
- Erratum
- Erratum to: Invariant subspace method: A tool for solving fractional partial differential equations, in: FCAA-20-2-2017
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–Volume 21–3–2018)
- Research Paper
- Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces
- Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance
- The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces
- Parallel algorithms for modelling two-dimensional non-equilibrium salt transfer processes on the base of fractional derivative model
- Some iterated fractional q-integrals and their applications
- Lebesgue regularity for nonlocal time-discrete equations with delays
- Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions
- Error estimates of high-order numerical methods for solving time fractional partial differential equations
- The Laplace transform induced by the deformed exponential function of two variables
- Attractivity for fractional evolution equations with almost sectorial operators
- The multiplicity solutions for nonlinear fractional differential equations of Riemann-Liouville type
- Well-posedness of general Caputo-type fractional differential equations
- Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions
- Inverse source problem for a space-time fractional diffusion equation
- Erratum
- Erratum to: Invariant subspace method: A tool for solving fractional partial differential equations, in: FCAA-20-2-2017
