Journal ArticleDOI
Existence of mild solution for evolution equation with Hilfer fractional derivative
Haibo Gu,Juan J. Trujillo +1 more
Reads0
Chats0
TLDR
By noncompact measure method, some sufficient conditions are obtained to ensure the existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann-Liouville fractional derivatives.About:
This article is published in Applied Mathematics and Computation.The article was published on 2015-04-15. It has received 248 citations till now. The article focuses on the topics: Fractional calculus & Measure (mathematics).read more
Citations
More filters
Applied Mathematics and Computation
TL;DR: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions by introducing graphs representing the domain of integration of the integrals in each term.
Journal ArticleDOI
Ulam–Hyers–Rassias Stability for a Class of Fractional Integro-Differential Equations
TL;DR: In this article, the authors investigated the stability of Ulam-Hyers, Ulam−Hyers-Rassias, and semi-Ulam-Hyers-Hers for a particular class of fractional integro-differential equations.
Journal ArticleDOI
Almost sectorial operators on Ψ‐Hilfer derivative fractional impulsive integro‐differential equations
Kulandhivel Karthikeyan,Panjaiyan Karthikeyan,Haci Mehmet Baskonus,Kuppusamy Venkatachalam,Yu-Ming Chu +4 more
Journal ArticleDOI
Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions
TL;DR: In this paper, the authors established the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer's fixed point theorem and Banach contraction principle, and established the equivalent mixed-type integral for nonlocal condition.
Journal ArticleDOI
New results on nonlocal functional integro-differential equations via Hilfer fractional derivative
TL;DR: In this article, the existence of Hilfer fractional integro-differential equations with nonlocal conditions is discussed and an application is presented to validate the theoretical results, using M o ¼ nch fixed point theorem and techniques of noncompactness.
References
More filters
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Journal ArticleDOI
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
TL;DR: The decaying speed of the Lyapunov function can be more generally characterized which include the exponential stability and power-law stability as special cases.