Results 11 to 20 of about 692,681 (370)

Analysis of Fractional Differential Equations

Journal of Mathematical Analysis and Applications, 2002
The authors discuss the existence, uniqueness and structural stability of solutions to nonlinear differential equations of fractional order. They take the differential operators in the Riemann-Liouville sense and the initial conditions are specified according to Caputo's suggestion, in order to allow for an interpretation in a physically meaningful way.
Diethelm, Kai, Ford, Neville J.
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Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense [PDF]

Mathematics, 2022
In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
semanticscholar   +1 more source

On the Stability and Numerical Scheme of Fractional Differential Equations with Application to Biology

De Computis, 2022
The fractional differential equations involving different types of fractional derivatives are currently used in many fields of science and engineering. Therefore, the first purpose of this study is to investigate the qualitative properties including the ...
K. Hattaf
semanticscholar   +1 more source

Generalized fractional differential equations for past dynamic

AIMS Mathematics, 2022
Well-posedness of the terminal value problem for nonlinear systems of generalized fractional differential equations is studied. The generalized fractional operator is formulated with a classical operator and a related weighted space.
D. Baleanu, B. Shiri
semanticscholar   +1 more source

ON THE FRACTIONAL RICCATI DIFFERENTIAL EQUATION [PDF]

International Journal of Pure and Apllied Mathematics, 2016
In this paper, We tried to find an analytical solution of nonlinear Riccati conformable fractional differential equation. Fractional derivatives are described in the conformable derivative. The behavior of the solutions and the effects of different values of fractional order ? are presented graphically and table.
Hanalioğlu (Khaniyev), Tahir, Merdan, M.   +1 more
openaire   +2 more sources

Approximate solutions of linear time-fractional differential equations

Journal of Mathematics and Computer Science, 2022
In this research work, the numerical scheme for obtaining the linear time-fractional differential equations was considered and the nature of these time-fractional differential equations are in sense of Caputo.
R. Oderinu, J. Owolabi, M. Taiwo
semanticscholar   +1 more source

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

Symmetry, 2021
This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function ϑ. By means of a hybrid fixed point theorem
M. Abbas, M. Ragusa
semanticscholar   +1 more source

On Laplace transforms with respect to functions and their applications to fractional differential equations

Mathematical methods in the applied sciences, 2021
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called Ψ‐fractional calculus.
Hafiz Muhammad Fahad, M. Rehman, A. Fernandez   +2 more
semanticscholar   +1 more source

The amazing fractional Maclaurin series for solving different types of fractional mathematical problems that arise in physics and engineering

Partial Differential Equations in Applied Mathematics, 2023
Many applications and natural phenomena in the fields of physics and engineering are described by ordinary and partial differential equations. Therefore, obtaining solutions to these equations helps to analyze and understand the dynamics of these systems,
Marwan Alquran
doaj   +1 more source

The modified generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Schrödinger type

Results in Physics, 2023
This paper presents a modified version of the generalized Kudryashov method aimed at obtaining exact solutions for fractional partial differential equations of Schrödinger type.
Fushun Liu, Yuqiang Feng
doaj   +1 more source