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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Existence And Stability Results Of Nonlinear Fractional Differential Equations With Nonlinear Integral Boundary Condition On Time Scales, Vipin Kumar, Muslim Malik
Existence And Stability Results Of Nonlinear Fractional Differential Equations With Nonlinear Integral Boundary Condition On Time Scales, Vipin Kumar, Muslim Malik
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we establish the existence and uniqueness of the solution to a nonlinear fractional differential equation with nonlinear integral boundary conditions on time scales.We used the fixed point theorems due to Banach, Schaefer’s, nonlinear alternative of Leray Schauder’s type and Krasnoselskii’s to establish these results. In addition, we study Ulam-Hyer’s (UH) type stability result. At the end, we present two examples to show the effectiveness of the obtained analytical results.
A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, Ali Khalouta, Abdelouahab Kadem
A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, Ali Khalouta, Abdelouahab Kadem
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we propose a new method called the inverse fractional Shehu transform method to solve homogenous and non-homogenous linear fractional differential equations. Fractional derivatives are described in the sense of Riemann-Liouville and Caputo. Illustrative examples are given to demonstrate the validity, efficiency and applicability of the presented method. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature.
A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini
A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method.
The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi
The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we have applied Jacobi polynomial to solve Riccati differential equation of fractional order. To do so, we have presented a general formula for the Jacobi operational matrix of fractional integral operator. Using the Tau method, the solution of this problem reduces to the solution of a system of algebraic equations. The numerical results for the examples presented in this paper demonstrate the efficiency of the present method.