An efficient numerical method for nonlinear fractional differential equations based on the generalized Mittag‐Leffler functions and Lagrange polynomials
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DOI: 10.1002/mma.6852
Abstract: In this paper, an efficient numerical method is developed for solving a class of nonlinear fractional differential equations. The main idea is to transform the nonlinear fractional differential equations into a system of integral equations… read more here.
Keywords: nonlinear fractional; numerical method; method; fractional differential ... See more keywords
Investigation of a system of nonlinear fractional order hybrid differential equations under usual boundary conditions for existence of solution
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DOI: 10.1002/mma.6865
Abstract: This research work is related to investigate sufficient conditions for existence, uniquely of solution to a coupled system of nonlinear fractional order hybrid differential equations (NFOHDEs). With the help of Burton's fixed point theorem, we… read more here.
Keywords: nonlinear fractional; system nonlinear; fractional order; order hybrid ... See more keywords
On Nonlinear Fractional Integro–Differential Equations with Positive Constant Coefficient
Sign Up to like & getrecommendations! Published in 2019 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-019-1325-y
Abstract: The aim of this study is to investigate the existence and other properties of solution of nonlinear fractional integro–differential equations with constant coefficient. Also with the help of Pachpatte’s inequality, we prove the continuous dependence… read more here.
Keywords: constant coefficient; integro differential; nonlinear fractional; differential equations ... See more keywords
Existence And Controllability For Nonlinear Fractional Control Systems With Damping in Hilbert Spaces
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DOI: 10.1007/s10473-019-0118-5
Abstract: In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces. Our first step is to give the representation… read more here.
Keywords: systems damping; control; nonlinear fractional; fractional control ... See more keywords
Generalized Bernoulli Polynomials: Solving Nonlinear 2D Fractional Optimal Control Problems
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DOI: 10.1007/s10915-020-01213-0
Abstract: This work develops an optimization method based on a new class of basis function, namely the generalized Bernoulli polynomials (GBP), to solve a class of nonlinear 2-dim fractional optimal control problems. The problem is generated… read more here.
Keywords: control; bernoulli polynomials; nonlinear fractional; generalized bernoulli ... See more keywords
Exact solutions for nonlinear fractional differential equations using exponential rational function method
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DOI: 10.1007/s11082-017-0895-9
Abstract: Exponential rational function method is a relatively new mechanism to get exact solutions of nonlinear fractional differential equations. In this paper, fractional derivatives in the sense of Jumarie’s modified Riemann–Liouville are defined. Fractional complex transform… read more here.
Keywords: nonlinear fractional; function method; exponential rational; fractional differential ... See more keywords
Existence of three solutions for perturbed nonlinear fractional p-Laplacian boundary value systems with two control parameters
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DOI: 10.1007/s11868-020-00354-y
Abstract: In this paper, we use two control parameters to study a class of perturbed nonlinear fractional p-Laplacian differential systems, where we prove the existence of three weak solutions by using the variational method and Ricceri’s… read more here.
Keywords: fractional laplacian; two control; perturbed nonlinear; nonlinear fractional ... See more keywords
Eigenvalues for Iterative Systems of Nonlinear Fractional Order Boundary Value Problems with p-Laplacian
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DOI: 10.1007/s40819-016-0263-7
Abstract: In this paper, we determine the eigenvalue intervals of $$\lambda _1, \lambda _2, \ldots , \lambda _n$$λ1,λ2,…,λn for which the iterative system of nonlinear fractional order with p-Laplacian two-point boundary value problem has a positive… read more here.
Keywords: nonlinear fractional; boundary value; fractional order; eigenvalues iterative ... See more keywords
Existence Results for Non-instantaneous Impulsive Nonlinear Fractional Differential Equation Via Variational Methods
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DOI: 10.1007/s40840-019-00797-7
Abstract: In this article, we investigate a class of nonlinear fractional differential equations with non-instantaneous impulses. By means of critical point theory and variational methods, we prove that the existence and multiplicity of nontrivial solutions for… read more here.
Keywords: instantaneous impulsive; fractional differential; non instantaneous; nonlinear fractional ... See more keywords
An optimization technique for solving a class of nonlinear fractional optimal control problems: Application in cancer treatment
Sign Up to like & getrecommendations! Published in 2021 at "Applied Mathematical Modelling"
DOI: 10.1016/j.apm.2021.01.004
Abstract: Abstract This paper proposes an optimization method for solving a general form of nonlinear fractional optimal control problems (NFOCP) governed by nonlinear fractional dynamical systems and mixed conditions. A model for cancer treatment based on… read more here.
Keywords: optimization; fractional optimal; nonlinear fractional; optimal control ... See more keywords
On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations
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DOI: 10.1016/j.apnum.2018.11.003
Abstract: Abstract In this study, an optimal homotopy analysis approach will be described to deal with nonlinear fractional differential equations. The proposed approach presents a procedure to find an optimal auxiliary linear operator and the corresponding… read more here.
Keywords: nonlinear fractional; homotopy analysis; fractional differential; differential equations ... See more keywords