Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 11 of 11 for “"fractional derivatives"”.
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Numerical methods for fractional differential equations by new caputo and hadamard types operators
Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-Fabrizio operator, Caputo-Hadamard fractional …
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Nonlinear vibration analysis of viscoelastic plates with fractional damping
Fractional calculus has the history as long as the classical calculus, but up to recent years, less attention has been paid to this method due to its complexity and difficulties in dealing with fractional derivatives and fractional integrals. In the present study, the nonlinear vibration analysis …
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Wavelets operational methods for fractional differential equations and systems of fractional differential equations
… systems. A new operational matrix of fractional order derivative and integration based on this polynomial was also developed and used together with collocation method to solve FDEs, systems of FDEs and fractional order delay differential equations. Error bound for some of the …
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Application of the Lagrangian descriptors method to Hamiltonian systems with emphasis to models of barred galaxies
… dynamical system whose evolution is governed by fractional ordinary differential equations (FDEs) and showcase the utility of this method in qualitatively revealing phase space structures for systems described by FDEs. In our study, we implement two numerical techniques to integrate such systems, …
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Basic functional and geometric inequalities for the fractional order operators on homogenous Lie groups
… Lie groups. As for direct inequalities we obtain fractional Hardy, Sobolev, Hardy-Sobolev, Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg, logarithmic inequal- ities, Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. Also, we obtain the integer order …
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An improved data classification framework based on fractional particle swarm optimization
… research proposed an improved Mutually-Optimized Fractional PSO (MOFPSO) algorithm based on fractional derivatives and small step lengths to ensure convergence to global optima by supplying a fine balance between exploration and exploitation. The proposed algorithm is tested and verified for …
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Production Analysis in Tight/Shale Reservoirs Via Machine Learning Approaches
… decline characterization, integrating Caputo fractional derivatives to capture the heavy-tailed phenomena in production series, thus offering a balance between interpretability and predictive capability. Further, the thesis explores the competitive adsorption of CH4/CO2 in shale formations …
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Effects of fractional time derivatives in predator-prey models
This thesis is concerned with the effects of fractional derivatives in predator-prey like systems, including models of plant water interaction. In Chapter 3, a fractional order predator-prey model is introduced, and we show how fractional derivative order can change the system from monostable to …
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions
… -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems …
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Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis
… the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the …
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Characterisation and prediction of state of health of rechargeable batteries
… including constant phase elements (CPEs). The fractional order of a CPE is linked to battery state of health (SoH) and energy efficiency. This thesis shows that efficiency measurements with waveforms representative of real battery usage can be used to track battery SoH accurately.