4. Analytical Solution of Pantograph Equation with Incommensurate Delay
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Jayvant Patade
Abstract
Pantograph equation is a delay differential equation (DDE) arising in electrodynamics. This paper studies the pantograph equation with two delays. The existence, uniqueness, stability and convergence results for DDEs are presented. The series solution of the proposed equation is obtained by using Daftardar-Gejji and Jafari method and given in terms of a special function. This new special function has several properties and relations with other functions. Further, we generalize the proposed equation to fractional-order case and obtain its solution.
Abstract
Pantograph equation is a delay differential equation (DDE) arising in electrodynamics. This paper studies the pantograph equation with two delays. The existence, uniqueness, stability and convergence results for DDEs are presented. The series solution of the proposed equation is obtained by using Daftardar-Gejji and Jafari method and given in terms of a special function. This new special function has several properties and relations with other functions. Further, we generalize the proposed equation to fractional-order case and obtain its solution.
Chapters in this book
- Frontmatter i
- Preface of the Book of Proceedings of the Virtual Conference on Computational Science (VCCS-2016) v
- Contents vii
- List of contributing authors xi
- 1. Addressing the challenges of standalone multi-core simulations in molecular dynamics 1
- 2. Optical and magnetic properties of free-standing silicene, germanene and T-graphene system 23
- 3. Theoretical study of the electronic states of newly detected dications. Case of MgS2+ AND SiN2+ 71
- 4. Analytical Solution of Pantograph Equation with Incommensurate Delay 93
- 5. Computational chemistry applied to vibrational spectroscopy: A tool for characterization of nucleic acid bases and some of their 5-substituted derivatives 117
- 6. Mechanism of nucleophilic substitution reactions of 4-(4’-nitro)phenylnitrobenzofurazan ether with aniline in acetonitrile 153
- 7. Computational methods in preformulation study for pharmaceutical solid dosage forms of therapeutic proteins 163
- 8. Computational Investigation of Cationic, Anionic and Neutral Ag2AuN (N = 1–7) Nanoalloy Clusters 173
- 9. Evacuation simulation using Hybrid Space Discretisation and Application to Large Underground Rail Tunnel Station 191
- 10. DFT study of anthocyanidin and anthocyanin pigments for Dye-Sensitized Solar Cells: Electron injecting from the excited states and adsorption onto TiO2 (anatase) surface 205
- 11. Elemental Two-Dimensional Materials Beyond Graphene 219
- Index 229
Chapters in this book
- Frontmatter i
- Preface of the Book of Proceedings of the Virtual Conference on Computational Science (VCCS-2016) v
- Contents vii
- List of contributing authors xi
- 1. Addressing the challenges of standalone multi-core simulations in molecular dynamics 1
- 2. Optical and magnetic properties of free-standing silicene, germanene and T-graphene system 23
- 3. Theoretical study of the electronic states of newly detected dications. Case of MgS2+ AND SiN2+ 71
- 4. Analytical Solution of Pantograph Equation with Incommensurate Delay 93
- 5. Computational chemistry applied to vibrational spectroscopy: A tool for characterization of nucleic acid bases and some of their 5-substituted derivatives 117
- 6. Mechanism of nucleophilic substitution reactions of 4-(4’-nitro)phenylnitrobenzofurazan ether with aniline in acetonitrile 153
- 7. Computational methods in preformulation study for pharmaceutical solid dosage forms of therapeutic proteins 163
- 8. Computational Investigation of Cationic, Anionic and Neutral Ag2AuN (N = 1–7) Nanoalloy Clusters 173
- 9. Evacuation simulation using Hybrid Space Discretisation and Application to Large Underground Rail Tunnel Station 191
- 10. DFT study of anthocyanidin and anthocyanin pigments for Dye-Sensitized Solar Cells: Electron injecting from the excited states and adsorption onto TiO2 (anatase) surface 205
- 11. Elemental Two-Dimensional Materials Beyond Graphene 219
- Index 229
