Some new existence results for fractional partial random nonlocal differential equations with delay
Keywords:
random differential equation, left-sided mixed Riemann-Liouville integral, Caputo fractional order derivative, Darboux problemAbstract
The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with finite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness. An illustration is given to show the applicability of our results.
References
Abbas, Saïd, Dumitru Baleanu, and Mouffak Benchohra. "Global attractivity for fractional order delay partial integro-differential equations." Adv. Difference Equ. (2012): Article No. 62.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Saïd, and Mouffak Benchohra. "Darboux problem for perturbed partial differential equations of fractional order with finite delay." Nonlinear Anal. Hybrid Syst. 3, no. 4 (2009): 597-604.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Saïd, Mouffak Benchohra, John R. Graef, and Johnny Henderson. Implicit Fractional Differential and Integral Equations: Existence and Stability. Vol. 26 of De Gruyter Series in Nonlinear Analysis and Applications. Walter de Gruyter GmbH & Co KG, 2018.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Saïd, Mouffak Benchohra, and Gaston Mandata N’Guérékata. Topics in Fractional Differential Equations. Vol. 27 of Developments in Mathematics. Springer: New York, 2012.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Saïd, Mouffak Benchohra, and Gaston Mandata N’Guérékata. Advanced Fractional Differential and Integral Equations. Nova Science Publishers: New York, 2014.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Abbas, Said, Mouffak Benchohra, and Yong Zhou. "Darboux problem for tractional order neutral functional partial hyperbolic differential equations." Int. J. Dynam. Systems Differ. Equa. 2, no. 3-4 (2009): 301-312.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Adigüzel, Rezan Sevinik, et. al. "On the solution of a boundary value problem associated with a fractional differential equation." Math. Methods Appl. Sci. (2020): 1-12.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Adigüzel, Rezan Sevinik, et. al. "On the solutions of fractional differential equations via Geraghty type hybrid contractions." Appl. Comput. Math. 20, no. 2 (2021): 313-333.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Sevinik-Adıgüzel, Rezan, et. al. "Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions." Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115, no. 3 (2021): Paper No. 155.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Afshari, Hojjat, and Erdal Karapınar. "A discussion on the existence of positive solutions of the boundary value problems via psi-Hilfer fractional derivative on b-metric spaces." Adv. Difference Equ. (2020): Paper No. 616.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ahmad, Bashir, et. al. "Random solutions for generalized Caputo periodic and non-local boundary value problems." Foundations. 3, no. 2 (2023): 275-289.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ahmad, Bashir, et. al. Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities. Springer: Cham, 2017.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ahmad, Bashir, and Juan Jose Nieto. "Riemann-Liouville fractional differential equations with fractional boundary conditions." Fixed Point Theory 13, no. 2 (2012): 329-336.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Appell, Jürgen. "Implicit functions, nonlinear integral equations, and the measure of noncompactness of the superposition operator." J. Math. Anal. Appl. 83, no. 1 (1981): 251-263.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ayerbee Toledano, José María, Tomás Dominguez Benavides, and Genaro Lopez Acedo. Measures of Noncompactness in Metric Fixed Point Theory. Vol. 99 of Operator Theory: Advances and Applications. Birkhäuser: Basel–Boston–Berlin, 1997.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Baleanu, Dumitru, et. al. "Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions." AIMS Math. 8, no. 2 (2023): 2556-2575.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bharucha-Reid, Albert Turner. Random Integral Equations. Vol. 96 of Mathematics in Science and Engineering. Academic Press: New York, 1972.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bothe, Dieter. "Multivalued perturbation of m-accretive differential inclusions" Israel J. Math. 108 (1998): 109-138.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Engl, Heinz W. "A general stochastic fixed-point theorem for continuous random operators on stochastic domains" J. Math. Anal. Appl. 66, no. 1 (1978): 220-231.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Harikrishnan, Sugumaran, Elsayed Mohammed Elsayed, and Kuppusamy Kanagarajan. "Study on random Langevin differential equations with fractional derivative with respect to another function." Nonlinear Stud. 29, no. 4 (2022): 1079-1096.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Itoh, Shigeru. "Random fixed-point theorems with an application to random differential equations in Banach spaces." J. Math. Anal. Appl. 67, no. 2 (1979): 261-273.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Karapınar, Erdal, et. al. "On continuity of the fractional derivative of the timefractional semilinear pseudo-parabolic systems." Adv. Difference Equ. (2021): Paper No. 70.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Benchohra, Mouffak, et. al. "Controllability of second order functional random differential equations with delay." Mathematics 10, no. 7 (2022): Article No. 1120.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kilbas, Anatoly A., Hari Mohan Srivastava, and Juan J. Trujillo. Theory and Applications of Fractional Differential Equations. Vol. 204 of North-Holland Mathematics Studies. Amsterdam: Elsevier Science B.V, 2006.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ladde, Gangaram Shivlingappa, and Vangipuram Lakshmikantham. Random Differential Inequalities. New York: Academic Press, 1980.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Liu, Meng, Liangzhou Chen, and Xiao-Bao Shu. "The existence of positive solutions for phi-Hilfer fractional differential equation with random impulses and boundary
##plugins.generic.googleScholarLinks.settings.viewInGS##
value conditions." Waves Random Complex Media. (2023): 1-19.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Liu, Lishan, et. al. "Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces." J. Math. Anal. Appl. 309, no. 2 (2005): 638-649.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Mönch, Harald. "Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces." Nonlinear Anal. 4, no. 5 (1980): 985-999.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Podlubny, Igor. Fractional differential equations. San Diego: Academic Press, 1999.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Salim, Abdelkrim, et. al. "Global stability results for Volterra-Hadamard random partial fractional integral equations." Rend. Circ. Mat. Palermo (2) 72, no. 3 (2023): 1783-1795.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Salim, Abdelkrim, et. al. "On k-Generalized psi-Hilfer Impulsive Boundary Value Problem with Retarded and Advanced Arguments." J. Math. Ext. 15 (2021): Paper no. 20.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Salim, Abdelkrim, et. al. "Boundary value problem for nonlinear implicit generalized Hilfer-type fractional differential equations with impulses." Abstr. Appl. Anal. (2021): Art. ID 5592010.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Salim, Abdelkrim, et. al. "Initial value problem for hybrid psi-Hilfer fractional implicit differential equations" J. Fixed Point Theory Appl. 24, no. 1 (2022): Paper No. 7.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Salim, Abdelkrim, Mokhtar Boumaaza, and Mouffak Benchohra. "Random solutions for mixed fractional differential equations with retarded and advanced arguments." J. Nonlinear Convex Anal. 23, no. 7 (2022): 1361-1375.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Tsokos, Chris Peter, and William Jowayne Padgett. Random Integral Equations with Applications to Life Sciences and Engineering. New York: Academic Press, 1974.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Vityuk, Aleksandr N., and A. V. Golushkov. "Existence of solutions of systems of partial differential equations of fractional order." Nonlinear Oscil. 7, no. 3 (2004): 328-335.
##plugins.generic.googleScholarLinks.settings.viewInGS##
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