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Computational analysis of fractional vibrational equations

  • S. Priyadharsini
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Advances in Mathematical and Computational Sciences
Ein Kapitel aus dem Buch Advances in Mathematical and Computational Sciences

Abstract

Fractional vibrational equations have emerged as a powerful tool for modeling complex systems with non-local and memory-dependent vibrational behaviors. This computational analysis explores methods and techniques employed to solve fractional vibrational equations, enabling a deeper understanding of dynamic systems. In this work, a brief overview of the recent results of fractional differential equations and the analytical methods used is given. We delve into analytical method, Laplace transform technique, numerical approaches, generalized Euler’s method, and specialized algorithms designed for fractional calculus. The solution of non-linear fractional system and its convergence are discussed. Some insightful illustrations are proposed to validate of the given theory. Recent updates highlight advancements in machine learning applications and interdisciplinary research, expanding the scope of fractional vibrational equations in fields such as structural engineering, materials science, and biophysics. The abstract encapsulates the ongoing efforts to develop robust computational tools, contributing to a more comprehensive exploration of fractional vibrational phenomena and their practical implications across diverse scientific disciplines.

Abstract

Fractional vibrational equations have emerged as a powerful tool for modeling complex systems with non-local and memory-dependent vibrational behaviors. This computational analysis explores methods and techniques employed to solve fractional vibrational equations, enabling a deeper understanding of dynamic systems. In this work, a brief overview of the recent results of fractional differential equations and the analytical methods used is given. We delve into analytical method, Laplace transform technique, numerical approaches, generalized Euler’s method, and specialized algorithms designed for fractional calculus. The solution of non-linear fractional system and its convergence are discussed. Some insightful illustrations are proposed to validate of the given theory. Recent updates highlight advancements in machine learning applications and interdisciplinary research, expanding the scope of fractional vibrational equations in fields such as structural engineering, materials science, and biophysics. The abstract encapsulates the ongoing efforts to develop robust computational tools, contributing to a more comprehensive exploration of fractional vibrational phenomena and their practical implications across diverse scientific disciplines.

Kapitel in diesem Buch

  1. Frontmatter I
  2. About the book VII
  3. Preface IX
  4. Contents XI
  5. About the Editors XV
  6. Logarithmic third Hankel determinant for a subclass of starlike functions 1
  7. Effect of gyrotactic microorganisms in rotating magnetic nanofluids in porous media 17
  8. Some applications of graph spectrum in post quantum cryptography 31
  9. Finite-time stability analysis of neutral type delay Cohen–Grossberg neural network with discontinuous activation function 47
  10. Influence of temperature modulation over heat/mass transport of Rivlin–Ericksen viscoelastic nanoliquid in Hele-Shaw cell 57
  11. On an operator preserving polynomial inequality of Paul Turán 75
  12. Effect of interaction between two finite faults on ground deformation 85
  13. On the number of bounded regions generated by a class of paths in the complex plane 111
  14. Binomial and de Moivre revisited through differential equations 125
  15. Modified projection method for second kind Fredholm integral equations with trigonometric polynomials 131
  16. Effect of heat and mass transfer in binary nanofluids (for silver nanoparticles) saturated in porous medium under the influence of LTNE model and different gravity modulation 145
  17. A comparative analysis of standard Knapsack and Legendre–Knapsack cryptosystem 169
  18. Study of creep in composite functionally graded disc with non-linear thickness 179
  19. On the h(hv)-torsion tensor and the v-curvature tensor of Matsumoto change with an h-vector 189
  20. Software reliability growth model considering power-law testing effort using optimization on hybrid PSO-GWO algorithm 199
  21. On near-perfect numbers with five prime factors 207
  22. Eulerian integrals associated with the product of multivariable H-function and generalized M-series 221
  23. Upper bounds for the complex growth rates in the Darcy–Brinkman convection in a binary viscoelastic fluid in a saturated porous layer 233
  24. Some result of fixed-point theorems in complete M-fuzzy metric space 243
  25. FR-labeling on hybrid partition shell graphs 261
  26. On essential M-Artinian modules 269
  27. Properties of reductions of multiplication modules 275
  28. Computational analysis of fractional vibrational equations 285
  29. Analysis of modified fractional order Lotka–Volterra model 307
  30. Topological indices of two chemical compounds used for drugs in the treatment of H1N1 335
  31. On the Gaussian higher-order Mersenne numbers 355
  32. Petri net: modeling, properties and analysis techniques 367
  33. An inventory system with time-dependent linear demand for deteriorating items under uncertainty with a completely backlogged 379
  34. On ∗-reverse derivations of involutive rings 389
  35. More functions via soft pre∗-generalized closed sets 397
  36. Modeling of piston problem for generalized Chaplygin gas 409
  37. A new estimation of the degree of approximation of functions belonging to Lipschitz class by Borel–Euler summability method of Fourier series 421
  38. Modeling the effect of discrete delay in SIR epidemic model with logistic growth 429
  39. Simple harmonic motion in view of quantum calculus 455
  40. On Bernstein and Turán-type inequalities for polynomials 461
  41. A weak and strong form of Ng ∗ b-continuous function in nano topological space 473
  42. Securing networks with graph theory: an approach to cyber security 483
https://doi.org/10.1515/9783111313634-023

Kapitel in diesem Buch

  1. Frontmatter I
  2. About the book VII
  3. Preface IX
  4. Contents XI
  5. About the Editors XV
  6. Logarithmic third Hankel determinant for a subclass of starlike functions 1
  7. Effect of gyrotactic microorganisms in rotating magnetic nanofluids in porous media 17
  8. Some applications of graph spectrum in post quantum cryptography 31
  9. Finite-time stability analysis of neutral type delay Cohen–Grossberg neural network with discontinuous activation function 47
  10. Influence of temperature modulation over heat/mass transport of Rivlin–Ericksen viscoelastic nanoliquid in Hele-Shaw cell 57
  11. On an operator preserving polynomial inequality of Paul Turán 75
  12. Effect of interaction between two finite faults on ground deformation 85
  13. On the number of bounded regions generated by a class of paths in the complex plane 111
  14. Binomial and de Moivre revisited through differential equations 125
  15. Modified projection method for second kind Fredholm integral equations with trigonometric polynomials 131
  16. Effect of heat and mass transfer in binary nanofluids (for silver nanoparticles) saturated in porous medium under the influence of LTNE model and different gravity modulation 145
  17. A comparative analysis of standard Knapsack and Legendre–Knapsack cryptosystem 169
  18. Study of creep in composite functionally graded disc with non-linear thickness 179
  19. On the h(hv)-torsion tensor and the v-curvature tensor of Matsumoto change with an h-vector 189
  20. Software reliability growth model considering power-law testing effort using optimization on hybrid PSO-GWO algorithm 199
  21. On near-perfect numbers with five prime factors 207
  22. Eulerian integrals associated with the product of multivariable H-function and generalized M-series 221
  23. Upper bounds for the complex growth rates in the Darcy–Brinkman convection in a binary viscoelastic fluid in a saturated porous layer 233
  24. Some result of fixed-point theorems in complete M-fuzzy metric space 243
  25. FR-labeling on hybrid partition shell graphs 261
  26. On essential M-Artinian modules 269
  27. Properties of reductions of multiplication modules 275
  28. Computational analysis of fractional vibrational equations 285
  29. Analysis of modified fractional order Lotka–Volterra model 307
  30. Topological indices of two chemical compounds used for drugs in the treatment of H1N1 335
  31. On the Gaussian higher-order Mersenne numbers 355
  32. Petri net: modeling, properties and analysis techniques 367
  33. An inventory system with time-dependent linear demand for deteriorating items under uncertainty with a completely backlogged 379
  34. On ∗-reverse derivations of involutive rings 389
  35. More functions via soft pre∗-generalized closed sets 397
  36. Modeling of piston problem for generalized Chaplygin gas 409
  37. A new estimation of the degree of approximation of functions belonging to Lipschitz class by Borel–Euler summability method of Fourier series 421
  38. Modeling the effect of discrete delay in SIR epidemic model with logistic growth 429
  39. Simple harmonic motion in view of quantum calculus 455
  40. On Bernstein and Turán-type inequalities for polynomials 461
  41. A weak and strong form of Ng ∗ b-continuous function in nano topological space 473
  42. Securing networks with graph theory: an approach to cyber security 483
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