The q-derivative and differential equation
The q-calculus appeared as a connection between mathematics and physics. It has several applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions, quantum theory, and electronics. Recently, a great interest to its applic...
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| Vydáno v: | Journal of physics. Conference series Ročník 1411; číslo 1; s. 12002 - 12009 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Bristol
IOP Publishing
01.11.2019
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| ISSN: | 1742-6588, 1742-6596 |
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| Abstract | The q-calculus appeared as a connection between mathematics and physics. It has several applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions, quantum theory, and electronics. Recently, a great interest to its applications in differential transform methods, in order to get analytical approximate solutions to the ordinary as well as partial differential equations. In this paper, we present some of the interesting definitions of q-calculus and q-derivatives. By using q-calculus, solutions of some differential equations could be generated. |
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| AbstractList | The q-calculus appeared as a connection between mathematics and physics. It has several applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions, quantum theory, and electronics. Recently, a great interest to its applications in differential transform methods, in order to get analytical approximate solutions to the ordinary as well as partial differential equations. In this paper, we present some of the interesting definitions of q-calculus and q-derivatives. By using q-calculus, solutions of some differential equations could be generated. The q -calculus appeared as a connection between mathematics and physics. It has several applications in different mathematical areas such as number theory, combinatorics, orthogonal polynomials, basic hypergeometric functions, quantum theory, and electronics. Recently, a great interest to its applications in differential transform methods, in order to get analytical approximate solutions to the ordinary as well as partial differential equations. In this paper, we present some of the interesting definitions of q -calculus and q -derivatives. By using q -calculus, solutions of some differential equations could be generated. |
| Author | Benbourenane, Jamal Akça, Haydar Eleuch, Hichem |
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| Cites_doi | 10.1103/PhysRevLett.76.1098 10.1007/BF00675167 10.1016/S0370-2693(98)01590-1 10.1016/0375-9601(94)91124-X 10.12693/APhysPolA.82.957 10.1142/S0217751X9600033X 10.1515/fascmath-2015-0014 10.1016/S0370-2693(98)01223-4 10.1016/S0375-9601(97)00068-6 10.1088/0305-4470/28/17/022 10.1016/S0898-1221(04)90025-9 |
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| References_xml | – volume: 76 start-page: 1098 year: 1996 ident: JPCS_1411_1_012002bib12 article-title: Quantum algebraic nature of the phonon spectrum in 4He publication-title: Physical review letters doi: 10.1103/PhysRevLett.76.1098 – volume: 33 start-page: 2019 year: 1994 ident: JPCS_1411_1_012002bib5 article-title: New q-derivative and q-logarithm publication-title: International Journal of theoretical physics doi: 10.1007/BF00675167 – volume: 448 start-page: 1 year: 1999 ident: JPCS_1411_1_012002bib18 article-title: Effect of q-deformation in the NJL gap equation publication-title: Phys. Lett. B doi: 10.1016/S0370-2693(98)01590-1 – volume: 185 start-page: 446 year: 1994 ident: JPCS_1411_1_012002bib15 article-title: Linearization and solutions of the discrete Painleve III equation publication-title: Physics letters A doi: 10.1016/0375-9601(94)91124-X – year: 1988 ident: JPCS_1411_1_012002bib17 – volume: 82 start-page: 957 year: 1992 ident: JPCS_1411_1_012002bib2 article-title: On the q-analogue of a black body radiation publication-title: Acta Phys. Polon. A doi: 10.12693/APhysPolA.82.957 – volume: 10 start-page: 15 year: 2017 ident: JPCS_1411_1_012002bib13 article-title: The presentation of a new type of quantum calculus publication-title: Tiblisi Mathematical Journal – year: 2001 ident: JPCS_1411_1_012002bib7 – volume: 11 start-page: 733 year: 1996 ident: JPCS_1411_1_012002bib14 article-title: Gauge theory publication-title: Internat. J. Modern Phys. A doi: 10.1142/S0217751X9600033X – volume: 55 start-page: 53 year: 2015 ident: JPCS_1411_1_012002bib8 article-title: A Note on q–Calculus publication-title: Fasciculi Mathematici doi: 10.1515/fascmath-2015-0014 – volume: 442 start-page: 82 year: 1998 ident: JPCS_1411_1_012002bib6 article-title: Superluminal propagation of light in gravitational field and non-causal signals publication-title: Phys. Lett. B doi: 10.1016/S0370-2693(98)01223-4 – volume: 135 start-page: x+ year: 1998 ident: JPCS_1411_1_012002bib4 article-title: Basic almost-poised hypergeometric series publication-title: Mem. Amer.Math. Soc. – volume: 41 start-page: 193 year: 1910 ident: JPCS_1411_1_012002bib10 article-title: On q-definite integrals publication-title: Quart. J. Pure and Appl. Math. – volume: 9 start-page: 19 ident: JPCS_1411_1_012002bib3 article-title: Euler-type Boundary value problems in quantum calculus publication-title: International Journal of Applied Mathematics and Statistics (IJAMAS) – volume: 227 start-page: 227 year: 1997 ident: JPCS_1411_1_012002bib16 article-title: Kinetic model for q-deformed bosons and fermions publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(97)00068-6 – volume: 28 start-page: 4915 year: 1995 ident: JPCS_1411_1_012002bib1 article-title: Phase transition in a q-deformed Lipkin model publication-title: J. Phys. A doi: 10.1088/0305-4470/28/17/022 – volume: 47 start-page: 281 ident: JPCS_1411_1_012002bib9 article-title: Integral inequalities in q-calculus publication-title: Computers and Mathematics with Applications doi: 10.1016/S0898-1221(04)90025-9 – year: 2002 ident: JPCS_1411_1_012002bib11 |
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| SubjectTerms | Calculus Combinatorial analysis Differential calculus Hypergeometric functions Mathematical analysis Number theory Partial differential equations Physics Polynomials Quantum theory |
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| Title | The q-derivative and differential equation |
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