Results 31 to 40 of about 1,126,367 (350)
Weak Solutions for Time-Fractional Evolution Equations in Hilbert Spaces
Fractal and Fractional, 2021 Our purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative.
Paola Loreti, Daniela Sforza
doaj +1 more source
Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]
, 2012 In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K. +6 more
core +1 more source
AIMS Mathematics, 2020 In present paper, we introduced generalized iterative method to solve linear and nonlinear fractional differential equations with composite fractional derivative operator.
Krunal B. Kachhia +1 more
doaj +1 more source
Existence of solutions for double-order Hilfer fractional boundary value problems at resonance
Journal of Hebei University of Science and Technology, 2022 In order to expand the basic theory of boundary value problems of fractional differential equations,the existence of solutions of double-order Hilfer fractional differential equations under Riemann-Stieltjes integral boundary conditions under resonance ...
Fanmeng MENG, Weihua JIANG, Chunjing GUO
doaj +1 more source
On solutions of fractal fractional differential equations
Discrete and Continuous Dynamical Systems. Series A, 2021 New class of differential and integral operators with fractional order and fractal dimension have been introduced very recently and gave birth to new class of differential and integral equations.
A. Atangana, Ali Akgül
semanticscholar +1 more source
International Journal of Differential Equations, 2016 This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations ...
Khalid Hilal, Ahmed Kajouni
doaj +1 more source
Stability analysis of multi-term fractional-differential equations with three fractional derivatives [PDF]
, 2020 Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties are obtained ...
arxiv +1 more source
Analysis of Fractional Differential Equations
, 2002 We discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order. The differential operators are taken in the Riemann–Liouville sense and the initial conditions are specified according to ...
K. Diethelm, N. Ford
semanticscholar +1 more source
Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations [PDF]
Mathematical methods in the applied sciences, 2020 In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving Ψ‐Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions.
Ashwini D. Mali, Kishor D. Kucche
semanticscholar +1 more source
Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations
Abstract and Applied Analysis, 2013 The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations.
Ahmet Bekir +2 more
doaj +1 more source