Showing 1-25 of 4,353 resultsfor "Index Terms":Fractional Differential Equations
"Index Terms":Fractional Differential Equations
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This paper proves the requirement of a time-varying initialization for fractional differential equations. This then requires a new definition for the fractional differintegral that includes the initialization and a new form of the Laplace transform of the fractional differintegral. An initialized fractional system theory is developed.Show More
Analytical solution of non-constant coefficients fractional differential equation by Adomian decomposition method
2012 24th Chinese Control and Decision Conference (CCDC)
Year: 2012 | Conference Paper |
In this paper, we attempt to solve a kind of fractional-order differential equations with non-constant coefficients by Adomian decomposition method. By showing two concrete examples, we find that Adomian decomposition method is also effective for the fractional-order differential equation with non-constant coefficients.Show More
Numerical Approach for Finding the Solution of Single Term Nonlinear Fractional Differential Equation
Ramashis Banerjee;Debottam Mukherjee;Pabitra Kumar Guchhait;Samrat Chakraborty;Joydeep Bhunia;Arnab Pal
2020 IEEE 1st International Conference for Convergence in Engineering (ICCE)
Year: 2020 | Conference Paper |
Here in this paper nonlinear fractional differential equation and its solution have been presented. Fractional Calculus is nothing but the generalization of integer order calculus and due to its complexity, it has not explored much but nature understands the language of fractional calculus more than classical calculus which helps it to find its application in every field of science and technology....Show More
In this research, the analysis of active circuit in the fractional domain has been performed by using the fractional differential equation approach. The derivative term within the fractional differential equation of the circuit has been interpreted in Caputo's sense and the analytical solution has been determined with the aid of Laplace transformation. By applying different source terms to the obt...Show More
An optimized MATLAB tool for efficient evaluation of fractional-order differential equations of time-varying orders
2021 American Control Conference (ACC)
Year: 2021 | Conference Paper |
A usage and benchmarks for a new proposed MATLAB tool for efficient evaluation of fractional-order backward differences, sums, differintegrals, and fractional-order differential equations (FODE) are presented in this paper. The tool also supports solving the generalized differential equations formulated with the time-varying fractional orders (VFODE), commonly employed, e.g., in the algorithm of a...Show More
Solution of Linear Fractional Fredholm Integro-Differential Equation by Using Second Kind Chebyshev Wavelet
2014 11th International Conference on Information Technology: New Generations
Year: 2014 | Conference Paper |
Cited by: Papers (6)
In the present paper, a numerical method is proposed to solve the fractional Fredholm integro-differential equation. The proposed method is based on the Chebyshev wavelet approximation. Using the approximation of an unknown function, its fractional derivative and its Integral operator in terms of Chebyshev wavelet, the fractional Fredholm integro-differential equation is ultimately reduced to a sy...Show More
Solvability for a class of nonlinear fractional differential equations with parameters
2018 18th International Conference on Control, Automation and Systems (ICCAS)
Year: 2018 | Conference Paper |
This paper investigates the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations with parameters. By using the properties of the Green function and Guo-Krasnosel'skii fixed point theorem, the eigenvalue intervals of boundary value problem of fractional differential equation are studied and some sufficient conditions for the existence and non...Show More
Some new exact solutions to fractional potential Korteweg-de Vries equation
2019 International Conference on Applied and Engineering Mathematics (ICAEM)
Year: 2019 | Conference Paper |
The objective of this paper is to find the exact soliton solutions to a nonlinear fractional partial differential equation (known as fractional potential Korteweg-de Vries (fp-KdV) equation). We have made use of complex wave transformation with Jumarie's Riemann-Liouville (R-L) derivative to convert fp-KdV into corresponding fractional ODE. This process is a part of fractional sub-equation method ...Show More
Solvability of boundary value problems of singular nonlinear fractional differential equations
2016 IEEE International Conference on Information and Automation (ICIA)
Year: 2016 | Conference Paper |
In this paper, we study the existence of positive solutions for the singular nonlinear fractional differential equation boundary value problem Dα0+ u(t) = f (t, u(t)), 0 <;t<; 1, u(0) = u(1) = u'(0) = u (1) = 0 where 3 <; α <; 4 is a real number, Dα0+ is the Riemann-Liouville fractional derivative, and f : (0, 1] × [0, +∞) → [0,+∞) is continuous, limt→0+f(t,.) = +∞ (i.e., f is singular at t = 0). ...Show More
Solving Fractional Riccati Differential Equations Using Haar Wavelet
2010 Third International Conference on Information and Computing
Year: 2010 | Conference Paper |
Cited by: Papers (6)
Using the Haar wavelets to expand the input signal and the output signal, then using the generalized Haar wavelet operational matrix of integration, we present a method to solve numerically the fractional Riccati differential equations. The results of the comparison with other methods indicate that the proposed method is simple and feasible.Show More
Approximate controllability of fractional stochastic integro-differential equations with infinite delay of order 1 < α < 2
This paper is mainly concerned with the approximate controllability of fractional stochastic integro-differential equations with infinite delay of order $1< \alpha < 2$. Sufficient conditions for approximate controllability of fractional control system are proved under a range condition on the control operator and the corresponding linear fractional control system is approximately controllable. Th...Show More
Fractional Interpretation of Anomalous Diffusion and Semiconductor Equations
2012 International Symposium on Electronic System Design (ISED)
Year: 2012 | Conference Paper |
Cited by: Papers (1)
Fractional calculus is considered as an effective tool in representing differential equations and systems. Fractional differential equations are generalizations of ordinary differential equations to an arbitrary non integer order. The idea of Fractional Differential Equations are used to analyse the semiconductor equations. Application of fractional calculus will add additional nonlinearity and ca...Show More
A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations
Rasool Shah;Hassan Khan;Umar Farooq;Dumitru Baleanu;Poom Kumam;Muhammad Arif
In this research article, a new analytical technique is implemented to solve system of fractional-order partial differential equations. The fractional derivatives are carried out with the help of Caputo fractional derivative operator. The direct implementation of Mohand and its inverse transformation provide sufficient easy less and reliability of the proposed method. Decomposition method along wi...Show More
Numerical Analysis for the Variable Order Time Fractional Diffusion-Wave Equation
2020 5th IEEE International Conference on Big Data Analytics (ICBDA)
Year: 2020 | Conference Paper |
Time fractional order partial derivative equations are the generalization of the traditional integer order partial derivative equations, in which the time fractional order derivative is used to replace the corresponding integer order derivative. In this paper, the variable order time fractional diffusion-wave equation is considered. Firstly, numerical approximation scheme has been proposed by usin...Show More
A Linearized Stability Theorem for Nonlinear Delay Fractional Differential Equations
In this paper, we prove a theorem of linearized asymptotic stability for nonlinear fractional differential equations with a time delay. By using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first method), we show that an equilibrium of a nonlinear Caputo fractional delay differential equation is asymptotically stable if its linearization at the equilibrium is asym...Show More
A Study on Advanced Techniques for Fractional Differential Equations: Integrating the Frobenius Method, ZZ Transform, and Diverse Machine Learning Approaches
Prabakaran Raghavendran;Tharmalingam Gunasekar;Saikat Gochhait
2024 5th International Conference on Data Analytics for Business and Industry (ICDABI)
Year: 2024 | Conference Paper |
This study explores fractional differential equations using fractional calculus techniques, extending the traditional Frobenius method with approaches like the ZZ transform and binomial series expansions. It presents efficient techniques for solving such equations and provides examples of their use in problem solving. Also, the study uses machine learning methodologies to solve approximate solutio...Show More
The Existence of Solutions for an Initial Value Problem of Caputo-katugampola Fractional Differential Equations
2018 4th International Conference on Green Technology and Sustainable Development (GTSD)
Year: 2018 | Conference Paper |
In this paper, the existence and uniqueness results of solution for an initial value problem of fractional differential equations with a new concept of fractional derivative in the case of the order α ϵ (1,2) have been investigated. This concept is based on the Caputo fractional derivative and Caputo-Hadamard fractional derivative into a single form. Banach's contraction mapping principle is used ...Show More
In this paper we consider a kind of polynomials-Legendre polynomials then we get Legendre wavelet. Legendre wavelet operational matrix of the fractional integration is derived and combined the property of operational matrix to solve nonlinear fractional differential equations, we give some example and the numerical example shows that the method is effective.Show More
Solving fractional partial differential equations in fluid mechanics by generalized differential transform method
Xuehui Chen;Liang Wei;Jizhe Sui;Xiaoliang Zhang;Liancun Zheng
2011 International Conference on Multimedia Technology
Year: 2011 | Conference Paper |
Cited by: Papers (8)
In this paper, the generalized differential transform method is implemented for solving several linear fractional partial differential equations arising in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. Numerical illustrations of the time-fractional diffusion equation and the time-fractional wave equation are inves...Show More
Controllability of fractional neutral functional differential equations with infinite delay driven by fractional Brownian motion
In this work, we establish a controllability result for a class of fractional neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion. To attain our objective we adapt the argument of Lakhel & McKibben (2018, Stochastics 90, no. 3, 313–329) where the existence of mild solutions to such stochastic equations was studied. An example is provided to...Show More
Analytical solutions of a time-fractional system of proportional delay differential equations
2017 2nd International Conference on Knowledge Engineering and Applications (ICKEA)
Year: 2017 | Conference Paper |
Cited by: Papers (1)
In our physical settings, most of the problems encountered are nonlinear in nature whose solutions can better be captured in fractional space. In this paper, a semi-analytical method is proposed for the approximate-analytical solutions of certain system of time-fractional differential equations (TFDDEs) prompted by proportional delays. The proposed semi-analytical technique is built on the basis o...Show More
Soliton Solutions for Space-Time Fractional Korteweg-De Vries Equation
2019 International Conference on Computing and Information Science and Technology and Their Applications (ICCISTA)
Year: 2019 | Conference Paper |
Cited by: Papers (1)
In this article, we established a traveling wave solutions for space-time fractional Korteweg-de Vries (KDV) by using the modified extended tanh method with the Riccati equation. Fractional complex transform and properties of modified Riemann-Liouville derivative have been used to reduce the nonlinear fractional partial differential equation into ordinary differential equation. The obtained exact ...Show More
Exact solutions of simple variational fractional equations on a finite time interval
MELECON 2008 - The 14th IEEE Mediterranean Electrotechnical Conference
Year: 2008 | Conference Paper |
Simple variational equation containing sum of left-sided and right-sided fractional derivatives is solved. The proposed method includes transformation of the operator of the equation to equivalent Riesz potential and application of composition rules for fractional integrals and derivatives. The general solution is explicitly derived for the homogeneous case and appears to be linear combination of ...Show More
Aspects of Fractional Calculus in RLC Circuits
Steliana V. Puşcaşu;Simona M. Bibic;Mihai Rebenciuc;Antonela Toma;Dragoş Şt. Nicolescu
2018 International Symposium on Fundamentals of Electrical Engineering (ISFEE)
Year: 2018 | Conference Paper |
Cited by: Papers (1)
This paper deals with applications of fractional calculus to electrical circuits, a special attention being given to RLC circuits. The main purpose of this paper is to determine and discuss the solution of the fractional RLC series circuit model in the form of a fractional integro-differential equation. The fractional solution obtained is analyzed comparing it with the solution obtained by other c...Show More
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