Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/a-study-on-impulsive-hilfer-fractional-evolution-equations-with-CgV67iv5DZ
References (39)
-
E. Gerolymatou, I. Vardoulakis, R. Hilfer (2006)
Modelling infiltration by means of a nonlinear fractional diffusion modelJournal of Physics D: Applied Physics, 39
-
Min Yang, Qiru Wang (2017)
Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditionsFractional Calculus and Applied Analysis, 20
-
Trifce Sandev, R. Metzler, Z. Tomovski (2011)
Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivativeJournal of Physics A: Mathematical and Theoretical, 44
-
(2012)
Existence and uniqueness for a problem involving Hilfer factional derivative -
P. Revathi, R. Sakthivel, Yong Ren (2016)
Stochastic functional differential equations of Sobolev-type with infinite delayStatistics & Probability Letters, 109
-
Jinrong Wang, Yong Zhou, Michal Feckan (2013)
Abstract Cauchy problem for fractional differential equationsNonlinear Dynamics, 71
-
R. Ibrahim (2010)
On the existence for diffeo-integral inclusion of Sobolev-type of fractional order with applicationsAnziam Journal, 52
-
Jin Liang, Ti‐Jun Xiao (2001)
Abstract Degenerate Cauchy Problems in Locally Convex SpacesJournal of Mathematical Analysis and Applications, 259
-
K. Furati, M. Kassim, N. Tatar (2012)
Existence and uniqueness for a problem involving Hilfer fractional derivativeComput. Math. Appl., 64
-
E. Hernández, R. Sakthivel, Sueli Aki (2008)
Existence results for impulsive evolution differential equations with state-dependent delay., 2008
-
R. Hilfer (2000)
Applications Of Fractional Calculus In Physics -
R. Hilfer (2000)
FRACTIONAL TIME EVOLUTION -
S. Agarwal, D. Bahuguna (2006)
Existence of solutions to Sobolev-type partial neutraldifferential equationsJournal of Applied Mathematics and Stochastic Analysis, 2006
-
(2002)
Experimental evidence for fractional time evolution in glass materials -
Haide Gou, Baolin Li (2017)
Existence of mild solutions for fractional nonautonomous evolution equations of Sobolev type with delayJournal of Inequalities and Applications, 2017
-
V. Keyantuo, C. Lizama (2006)
Equations in Vector-valued Function Spaces -
R. Akhmerov, M. Kamenskiĭ, A. Potapov, A. Rodkina, B. Sadovskii (1992)
Measures of noncompactness and condensing operatorsOperator theory, 55
-
(1983)
On the behavior of measure of noncompactness with respect to differentiation and integration of vector-valued functions -
Lishan Liu, F. Guo, Congxin Wu, Yonghong Wu (2005)
Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spacesJournal of Mathematical Analysis and Applications, 309
-
Haide Gou, Baolin Li (2018)
Study on the mild solution of Sobolev type Hilfer fractional evolution equations with boundary conditionsChaos, Solitons & Fractals
-
Abd Elgadir, Ahmed Mohammed (2009)
Integral transforms and their applications -
T. Ke, C. Kinh (2014)
GENERALIZED CAUCHY PROBLEM INVOLVING A CLASS OF DEGENERATE FRACTIONAL DIFFERENTIAL EQUATIONS -
A. Benchaabane, R. Sakthivel (2017)
Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficientsJ. Comput. Appl. Math., 312
-
C. Lizama, Rodrigo Ponce (2011)
Periodic solutions of degenerate differential equations in vector-valued function spacesStudia Mathematica, 202
-
Haide Gou, Baolin Li (2018)
Study on Sobolev type Hilfer fractional integro-differential equations with delayJournal of Fixed Point Theory and Applications, 20
-
G. Barenblatt, I. Zheltov, I. Kochina (1960)
Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]Journal of Applied Mathematics and Mechanics, 24
-
H. Ahmed, M. El-Borai (2018)
Hilfer fractional stochastic integro-differential equationsAppl. Math. Comput., 331
-
H. Ahmed, M. El-Borai, H. El-Owaidy, A. Ghanem (2018)
Impulsive Hilfer fractional differential equationsAdvances in Difference Equations, 2018
-
K. Balachandran, S. Kiruthika, J. Trujillo (2011)
On fractional impulsive equations of Sobolev type with nonlocal condition in Banach spacesComput. Math. Appl., 62
-
(1989)
Ordinary differential equations in abstract spaces -
Haibo Gu, J. Trujillo (2015)
Existence of mild solution for evolution equation with Hilfer fractional derivativeAppl. Math. Comput., 257
-
Elizabeth Culotta (1995)
Endangered Species: Minimum Population Grows Larger, 270
-
(2000)
Applications of fractional caiculus in physics -
M. Kassim (2013)
NON-EXISTENCE OF GLOBAL SOLUTIONS FOR A DIFFERENTIAL EQUATION INVOLVING HILFER FRACTIONAL DERIVATIVE -
R. Hilfer, Yury Luchko, Z. Tomovski (2009)
OPERATIONAL METHOD FOR THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES -
(1996)
The positive solutions of abstract semilinear evolution equations and their applications -
Fang Li, Jin Liang, Hong-Kun Xu (2012)
Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditionsJournal of Mathematical Analysis and Applications, 391
-
K. Balachandran, E. Anandhi, J. Dauer (2003)
Boundary controllability of Sobolev-type abstract nonlinear integrodifferential systemsJournal of Mathematical Analysis and Applications, 277
-
Jinrong Wang, Yuruo Zhang (2015)
Nonlocal initial value problems for differential equations with Hilfer fractional derivativeAppl. Math. Comput., 266
- Publisher
- de Gruyter
- Copyright
- © 2020 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 2191-0294
- eISSN
- 2191-0294
- DOI
- 10.1515/ijnsns-2019-0015
- Publisher site
- See Article on Publisher Site
Abstract
AbstractIn this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results.
Journal
International Journal of Nonlinear Sciences and Numerical Simulation – de Gruyter
Published: Apr 26, 2020