The Laplace transform Induced by the Deformed Exponential Function of Two Variables
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 generalizati...
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| Veröffentlicht in: | Fractional calculus & applied analysis 2018-06, Vol.21 (3), p.775-785 |
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| container_title | Fractional calculus & applied analysis |
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| creator | Rajković, Predrag M. Stanković, Miomir S. Marinković, Sladjana D. |
| description | 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. |
| doi_str_mv | 10.1515/fca-2018-0040 |
| format | Article |
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| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Abstract Harmonic Analysis Analysis convolution Deformation Derivatives Differential equations differential operator exponential function Exponential functions fractional calculus Functional Analysis Integral equations integral transform Integral Transforms Integrals Kernel functions Laplace transforms Mathematics Operational Calculus Primary 44A10 Research Paper Secondary 33B10, 26A33 |
| title | The Laplace transform Induced by the Deformed Exponential Function of Two Variables |
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