... Laplace’s **differential** **equation** by using operational calculus in the framework of distribution ...that **differential** **equation** with an inhomogeneous term, and also a **fractional** ...

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... certain **fractional** **differential** ...of **fractional** order **differential** ...to **fractional** order **differential** **equation** using **fractional** Laplace Transform with initial ...

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... Ba?leanu et al Advances in Difference Equations 2012, 2012 145 http //www advancesindifferenceequations com/content/2012/1/145 R ES EA RCH Open Access On a fractional differential equation with infini[.] ...

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... nonlinear **fractional** **differential** **equation** with weighted initial and nonlocal condition and prove the existence and approximation of the ...nonlinear **fractional** **differential** ...

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... Abstract In the present paper the process of finding new solutions from previous solutions of a given **fractional** **differential** **equation** (FDE) is considered. For this issue, first we should construct ...

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... reduced **Fractional** **differential** **equation**. The **fractional** derivative is considered in the Caputo sense ...the **equation** into an integral ...to **fractional** **differential** ...

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... the **fractional** **differential** **equation** system can be converted into a problem in ordinary **differential** **equation** in two ...calculation **fractional** **differential** **equation** ...

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... class **fractional** **differential** **equation** with Robin and Dirichlet boundary ...the **differential** inequality method, oscillation criteria for a class of nonlinear **fractional** ...

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... of **fractional** order; for details, see ...to **fractional** diﬀerential equations and their systems, espe- cially coupled systems, were well studied by many authors; for details, see ...

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... The rest of the paper consists of the following sections. In Sect. 2, we present some preliminaries and lemmas to be used to prove our main result. In Sect. 3, we establish the existence and uniqueness theorems of ...

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... integral **equation** which is diﬀerent from the in- tegral **equation** [] and [] have obtained, and we apply the Schauder and Banach ﬁxed point theorems to prove the existence and uniqueness of solutions to ...

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... of **fractional** nonlocal multi-point boundary value problems of higher order **fractional** diﬀerential **equation**, this kind of problems arise from viscoelasticity, electrochemistry control, porous media, ...

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... Keywords: time fractional differential equations; mixed-index problems; analytical solution; 9.. asymptotic stability 10.[r] ...

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... O h ( 0 3 ). Additionally, we apply the numerical algorithm to solve the initial value problem involving a Riemann-Liouville **fractional** derivative. Numerical example shows that, the numerical scheme is ...

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... The ﬁrst-order deterministic and Brownian motion models do not ﬁt the CGM data. Al- though the deterministic higher-order integer and **fractional**-order models give much bet- ter ﬁts to the observed data than the ...

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... In this manuscript, by making use of ﬁxed point techniques on ordered metric spaces, the existence and uniqueness of the solution of a nonlinear **fractional** diﬀerential **equation** with periodic and ...

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... R **differential** equations of **fractional** order have recently proved to be valuable tools in the modeling of many phenomena in various fields of science and ...

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... This paper is organized as follows. in Section 2 we recall some definitions of **fractional** integral and derivative and related basic properties which will be used in the sequel. In Section 3, we deal with the ...

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... is the graph of the solution for λ = 1. Let us remark that if β = 1, and λ = 1 then the **equation** (8) is ordinary diﬀerential **equation** x ′ (t) = x(t) + t with the condition x(0) = 2. Its solution is x(t) = ...

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... Obviously, if we set α = in (.), one can obtain the Lyapunov classical inequality (.). In [], the same author studied a diﬀerential **equation** that depends on the Riemann- Liouville **fractional** ...

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