 |
 |
 |
 |
 |
 |
Sains Malaysiana 44(2)(2015): 295–300
Existence Results for a Family of Equations of Fractional Resolvent (Keputusan Kewujudan bagi Keluarga Persamaan Pecahan Berperingkat)
RABHA W. IBRAHIM*, SAYYEDAH A. QASEM & ZAILAN SIRI
Institute of
Mathematical Sciences, University Malaya, 50603 Kuala Lumpur, Malaysia
Diserahkan: 4
Jun 2014/Diterima: 25 Julai 2014
ABSTRACT
This study deals with
the presence and distinction of bounded m-solutions (type mild) for a family of
generalized integral and differential equations of spot order with fractional resolvent and indefinite delay.
Keywords: Fractional
calculus; fractional differential equations; fractional differential operator
ABSTRAK
Kajian ini membincangkan kehadiran dan perbezaan terbatas m-penyelesaian (jenis lembut) untuk keluarga integral umum dan persamaan pembezaan titik tertib dengan pecahan berperingkat dan lengah tak tentu.
Kata kunci: Kalkulus pecahan; pecahan pembezaan pengoperasi; persamaan pembezaan pecahan
RUJUKAN
Agarwal,
R.P., Ahmad, B., Alsaedi, A. & Al-Hutami, H. 2014. On nonlinear
fractional q-difference equations involving two fractional orders with
three-point non-local boundary conditions. Dyn. Contin. Discrete Im- puls. Syst. Ser. A Math. Anal.21:
135-151.
Agarwal,
R.P., dos Santos, J.P. & Cuevas, C. 2012. Analytic resolvent operator and existence
results for fractional integro-differential
equations. Journal of Abstract Differential Equations and
Applications 2(2): 26-47.
Araya,
D. & Lizama, C. 2008. Almost automorphic mild solutions to
fractional differential equations. Nonlinear Anal. 69: 3692-3705.
Arendt,
W., Batty, C.J., Hieber, M. & Neubrander,
F. 2011. Vector-valued Laplace
Transforms and Cauchy Problems.
2nd ed. Berlin: Birkhäuser, Springer. Cuevas,
C. & Lizama, C. 2008. Almost automorphic solutions to a class
of semi linear fractional differential equations. Appl. Math. Lett.21: 1315-1319.
Dhanapalan,
V., Thamilselvan, M. & Chandrasekaran,
M. 2014. Existence and uniqueness of mild
solutions for fractional integrodifferential equations. Appl. Comput Math-Bak. 3(1): 32-37.
Diagana, T.
2009. Existence of solutions to some classes of partial
fractional differential equations. Nonlinear Anal. 71: 5269-5300.
Hernandez,
E. & McKibben, M. 2005. Some
comments on: Existence of solutions of abstract nonlinear second order neutral
functional integro-differential equations. Comput. Math. Appl. 50: 655-669.
Ibrahim,
R.W. 2014. Solutions to systems of arbitrary -order differential equations in
complex domains. Electronic Journal of Differential Equations 46: 1-13.
Ibrahim,
R.W. 2013. Modified fractional Cauchy problem in a complex
domain. Advances in Difference Equations 149: 1-10.
Ibrahim,
R.W. 2012a. Complex transforms for system of fractional differential equations. Abstract and Applied Analysis Artical number 814759.
Ibrahim,
R.W. 2012b. Ulam stability for fractional differential equation in complex domain. Abstract and Applied Analysis Artical number 649517.
Ibrahim,
R.W. & Jalab, H.A. 2010. Existence of the solution of fractional integral inclusion
with time delay. Miskolic Mathematical Journal 2(11): 139-150.
Kilbas,
A.A., Srivastava, H.M. & Trujillo, J.J. 2006. Theory and Applications of Fractional Differential Equations. Vol. 204 (North-Holland, Mathematics Studies). Elsevier Science.
Martin,
R.H. 1987. Nonlinear Operators and Differential Equations
in Banach Spaces. Florida: Robert
E. Krieger Publ. Co.
Podlubny, I.
1999. Fractional Differential Equations. London:
Acad. Press.
Ponce,
R. 2013. Bounded mild solutions to fractional integro-differential equations in Banach spaces. Semigroup Forum 87: 377-392.
*Pengarang untuk surat-menyurat; email: rabhaibrahim@yahoo.com
|
|||
|
