Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel
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DOI: 10.1007/s10957-018-1305-6
Abstract: In this paper, we consider a diffusion equation with fractional time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. We first prove the existence and uniqueness of solution by means of a spectral argument. Then,… read more here.
Keywords: equation fractional; fractional time; nonsingular mittag; time derivative ... See more keywords
Periodic solutions of a semilinear elliptic equation with a fractional Laplacian
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DOI: 10.1007/s11784-016-0357-1
Abstract: We consider periodic solutions of the following problem associated with the fractional Laplacian $$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$(-∂xx)su(x)+F′(u(x))=0,u(x)=u(x+T),inR,where $$(-\partial _{xx})^s$$(-∂xx)s denotes the usual fractional Laplace operator with… read more here.
Keywords: equation fractional; solutions semilinear; periodic solutions; fractional laplacian ... See more keywords
Bifurcation of traveling waves and exact solutions of Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution
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DOI: 10.1007/s40314-019-0762-3
Abstract: The article is devoted in the study of the Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution in which modified Riemann–Liouville derivative is considered. We discuss the dynamical behavior of the system using bifurcation… read more here.
Keywords: modified equal; equation fractional; petviashvili modified; kadomtsev petviashvili ... See more keywords
An Efficient Method for Solving Singularly Perturbed Riccati Equation with Fractional Order
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DOI: 10.1007/s40819-017-0474-6
Abstract: In this paper, we study a class of singularly perturbed Riccati equation with fractional order. We divide the problem into three problems. The first problem is the reduced problem when $$\epsilon =0$$ϵ=0. The second and… read more here.
Keywords: singularly perturbed; equation fractional; fractional order; perturbed riccati ... See more keywords
Global Unsolvability of the Burgers Equation with Fractional Time Derivative
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DOI: 10.1134/s0012266119060156
Abstract: We obtain sufficient conditions for the nonexistence of time-global solutions of a fractional analog of the Burgers equation. Examples of solution blowup are considered for the Cauchy problem. The Mitidieri-Pokhozhaev nonlinear capacity method is used. read more here.
Keywords: time; burgers equation; equation fractional; unsolvability burgers ... See more keywords
Analysis of Fuzzy Differential Equation with Fractional Derivative in Caputo Sense
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DOI: 10.1155/2023/4009056
Abstract: In this article, the dynamics of the fuzzy fractional order enzyme Michaelis Menten model are investigated. To study problems with uncertainty, fuzzy fractional technique is applied. Using fuzzy theory, the sequential iterations of the model… read more here.
Keywords: fuzzy differential; differential equation; fractional derivative; analysis fuzzy ... See more keywords
The construction of solutions to Zakharov–Kuznetsov equation with fractional power nonlinear terms
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DOI: 10.1186/s13662-019-2063-y
Abstract: In the paper, we study a plasma fluid physical model, namely the Zakharov–Kuznetsov (ZK, for simplicity) equation with fractional power nonlinear terms by the complete discrimination system for polynomial method, and give a detailed construction… read more here.
Keywords: power nonlinear; nonlinear terms; equation fractional; equation ... See more keywords
Weak solutions for nonlinear fractional differential equation with fractional separated boundary conditions in Banach spaces
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DOI: 10.2298/fil1803117r
Abstract: This paper deals with nonlinear fractional differential equation with fractional separated boundary conditions. We investigate the existence of weak solutions in Banach spaces. To obtain such result we apply an appropriate fixed point theorem and… read more here.
Keywords: equation fractional; differential equation; separated boundary; nonlinear fractional ... See more keywords