دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات43
تعداد شماره‌ها1,253
تعداد مقالات15,411
تعداد مشاهده مقاله51,245,948
تعداد دریافت فایل اصل مقاله14,254,202
Mahammad, Khuddush, Benyoub, Mohammed, Kathun, Sarmila. (1403). Existence, uniqueness, and stability analysis of coupled random fractional boundary value problems with nonlocal conditions. سامانه مدیریت نشریات علمی, 12(1), 100-116. doi: 10.22034/cmde.2023.53235.2246
Khuddush Mahammad; Mohammed Benyoub; Sarmila Kathun. "Existence, uniqueness, and stability analysis of coupled random fractional boundary value problems with nonlocal conditions". سامانه مدیریت نشریات علمی, 12, 1, 1403, 100-116. doi: 10.22034/cmde.2023.53235.2246
Mahammad, Khuddush, Benyoub, Mohammed, Kathun, Sarmila. (1403). 'Existence, uniqueness, and stability analysis of coupled random fractional boundary value problems with nonlocal conditions', سامانه مدیریت نشریات علمی, 12(1), pp. 100-116. doi: 10.22034/cmde.2023.53235.2246
Mahammad, Khuddush, Benyoub, Mohammed, Kathun, Sarmila. Existence, uniqueness, and stability analysis of coupled random fractional boundary value problems with nonlocal conditions. سامانه مدیریت نشریات علمی, 1403; 12(1): 100-116. doi: 10.22034/cmde.2023.53235.2246

Existence, uniqueness, and stability analysis of coupled random fractional boundary value problems with nonlocal conditions

Computational Methods for Differential Equations
مقاله 9، دوره 12، شماره 1، فروردین 2024، صفحه 100-116    اصل مقاله (381.91 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.53235.2246
نویسندگان
Khuddush Mahammad* 1؛ Mohammed Benyoub2؛ Sarmila Kathun3
1Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Resapuvanipalem, Visakhapatnam, 530013, Andhra Pradesh, India.
2Department of Mathematics, Ecole Normale Sup\'{e}rieure, Taleb Abderrahmane de Laghouat, 03000 Laghouat, Algeria.
3Department of Applied Mathematics, Andhra University, Visakhapatnam, 530003, India.
چکیده
In this paper, the existence, uniqueness, compactness, and stability of a coupled random differential equations involving the Hilfer fractional derivatives with nonlocal boundary conditions are discussed. Arguments are discussed via some random fixed point theorems in a separable vector Banach spaces and Ulam type stability. Some examples are presented to ensure the abstract results.
کلیدواژه‌ها
Coupled fractional differential systems؛ Random variable؛ Hilfer fractional derivatives؛ Nonlocal conditions؛ Fixed point theorem؛ Ulam-Hyers stability
مراجع
  • [1] M. I. Abbas, Existence and uniqueness results for fractional differential equations with Riemann-Liouville frac- tional integral boundary conditions, Abstr. Appl. Anal. 290674 (2015), 1-6.
  • [2] S. Abbas, N. Al Arifi, M. Benchohra, and J. Graef, Random coupled systems of implicit Caputo-Hadamard fractional differential equations with multi-point boundary conditions in generalized Banach spaces, Dynam. Syst. Appl, 28(2) (2019), 229-350.
  • [3] S. Abbas, N. Al Arifi, M. Benchohra, and Y. Zhou, Random coupled Hilfer and Hadamard fractional differential systems in generalized Banach spaces, Mathematics, 7(3), (2019), 1-15.
  • [4] S.  Abbas,  M.  Benchohra,  and  G.  M.  N’Gu´er´e  kata,  Topics in fractional diferential equations,  Springer  Verlag, New York, 2012.
  • [5] S. Abbas, M. Benchohra, and J. Henderson, Coupled Caputo-Fabrizio fractional differential systems in generalized Banach spaces, Malaya Journal of Matematik, 9(1) (2021), 20-25.
  • [6] S. Abbas, M. Benchohra, J. E. Lazreg, and J. J. Nieto, On a coupled system of Hilfer and Hilfer-Hadamard fractional differential equations in Banach spaces, J. Nonlinear Funct. Anal, 12 (2018), 1-12.
  • [7] I. Altun, N. Hussain, M. Qasim, and H. H. Al-Sulami, A new fixed point result of Perov type and its application to a semilinear operator system, Mathematics, 7(11) (2019), 1-10.
  • [8] J. Alzabut, A. G. Selvam, D. Vignesh, and Y. Gholami, Solvability and stability of nonlinear hybrid ∆-difference equations of fractional order, Inter. J. Nonl. Sci. Num. Sim., 2021 Aug 20.
  • [9] E. H. Ait dads, M. Benyoub, and M. Ziane, Existernce results for Riemann- Liouville fractional evolution inclu- sions in Banach spaces, Afrika Matematika, 4 (2020), 709-715.
  • [10] G. Allaire and S. M. Kaber, Numerical linear algebra, Ser. Texts in Applied Mathematics, Springer, New York, 2008.
  • [11] S. Aljoudi, B. Ahmadand, and A. Alsaedi, Existence and uniqueness results for a coupled system of Caputo- Hadamard fractional differential equations with nonlocal Hadamard type integral boundary conditions, Fractal Fract., 4(13) (2020), 1-15.
  • [12] A. Baliki, J. J. Nieto, A. Ouahab, and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory and Applications, (2017), 1–29.
  • [13] A. T. Bharucha-Reid, Random Integral Equations, Academic Press, New York, (1972).
  • [14] M. Boumaaza, M. Benchohra, and J. Henderson, Random coupled Caputo-type modification of Erdelyi-Kober fractional differential systems in generalized Banach spaces with retarded and advanced arguments, 2021 (2021), 1–14.
  • [15] C. Burgos, J. C. Cortes, L. Villafuerte, and R. J. Villanueva, Solving random fractional second-order linear equations via the mean square Laplace transform: Theory and statistical computing, Applied Mathematics and Computation. 2022 Apr 1, 418:126846.
  • [16] K. Diethelm, Analysis of fractional differential equations, Springer, Berlin, 2010.
  • [17] A. M. El-Sayed AM, F. Gaafar, and M. El-Gendy, Continuous dependence of the solution of random fractional- order differential equation with nonlocal conditions, Fractional Differential Calculus, 1 (2017), 135-149.
  • [18] M. Q. Feng, X. M. Zhang, and W. G. Ge, New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions, Bound. Value Probl., 12(2011), Art. ID 720702, 1-20.
  • [19] C. Guendouz, J. E. Lazreg, J. J. Nieto, and A. Ouahab, Existence and compactness results for a system of fractional differential equations, Journal of Function Spaces, 5735140 (2020), 1-13.
  • [20] J. R. Graef, J. Henderson, and A. Ouahab, Topological methods for differential equations and inclusions, Mono- graphs and Research Notes in Mathematics Series Profile, CRC Press, Boca Raton, FL, 2019.
  • [21] Y. Hafssa and Z. Dahmani, Solvability for a sequential system of random fractional differential equations of Hermite type, Journal of Interdisciplinary Mathematics, 4(2022), 1-21.
  • [22] D. Henry, Geometric theory of semilinear parabolic differential equations, Springer, Berlin, New York, 1989.
  • [23] N. Heymans and I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives, Rheol. Acta., 45 (2006), 765-771.
  • [24] R. Hilfer, Applications of fractional calculus in Physics, World Scientific, Singapore, 2000.
  • [25] R. Hilfer, Y. Luchko, and Tomovski, Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives, Fract. Calc. Appl. Anal., 12(3) (2009), 299-318.
  • [26] S. Jabeen, Z. Zheng, M. U. Rehman, W. Wei, and J. Alzabut, Some fixed point results of weak-fuzzy graphical contraction mappings with application to integral equations, Mathematics, 9(5) (2021), 1-16.
  • [27] F. Jarad, S. Harikrishna, K. Shah, and K. Kanagarajan, Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative, Discrete and Continuous Dynamical Systems Series S, 13(3) (2020), 1-17.
  • [28] T. Jin, S. Gao, H. Xia, and H. Ding, Reliability analysis for the fractional-order circuit system subject to the uncertain random fractional-order model with Caputo type, Journal of Advanced Research, 32 (2021), 15-26.
  • [29] M. K. A. Kaabar, A. Refice, M. S. Souid, F. Mart´ınez, S. Etemad, Z. Siri, and S. Rezapour, Existence and UHR stability of solutions to the implicit nonlinear FBVP in the variable order settings, Mathematics, 9(14) (2021), 1-23.
  • [30] M. K. A. Kaabar, M. Shabibi, J. Alzabut, S. Etemad, W. Sudsutad, F. Martinez, and S. Rezapour, Investigation of the fractional strongly singular thermostat model via fixed point techniques, Mathematics, 9(18) (2021), 2298.
  • [31] M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing multivalued maps and semilinear differential inclusions in Banach spaces, De Gruyter, Berlin, 2001.
  • [32] M. Khuddush, Existence of solutions to the iterative system of nonlinear two-point tempered fractional order boundary value problems, Advanced Studies: Euro-Tbilisi Mathematical Journal, 16(2) (2023), 97–114.
  • [33] M. Khuddush and K. R. Prasad, Infinitely many positive solutions for an iterative system of conformable fractional order dynamic boundary value problems on time scales, Turk. J. Math., (2021). DOI: 10.3906/mat-2103-117
  • [34] M. Khuddush and K. R. Prasad, Existence, uniqueness and stability analysis of a tempered fractional order thermistor boundary value problems, The Journal of Analysis, (2022), 1-23.
  • [35] M. Khuddush and K. R. Prasad, Iterative system of nabla fractional fractional difference equations with two-point boundary conditions, Math. Appl., 11 (2022), 57-74.
  • [36] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
  • [37] G. S. Ladde and V. Lakshmikantham, Random Differential Inequalities, Academic Press, New York, (1980).
  • [38] S. Muthaiah, J. Alzabut, D. Baleanu, M. E. Samei, and A. Zada, Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions, Adv. Diff. Equa., 2021(1) (2021), 1-46.
  • [39] S. Nageswara Rao, A. H. Msmali, M. S. Abdullah Ali, and H. Ahmadini, Existence and uniqueness for a system of Caputo-Hadamard fractional differential equations with multipoint boundary conditions, Journal of Function Spaces, 2020 (2020), 1-10.
  • [40] O. Nica, Initial-value problems for first-order differential systems with general nonlocal conditions, Elect. J. Differ. Equa., 2012 (2012), 1-15.
  • [41] D. O’Regan and R. Precup, Theorems of Leray-Schauder type and applications, Gordon and Breach, Amsterdam, 2021.
  • [42] K. R. Prasad, M. Khuddush, and D. Leela, Existence of solutions for n-dimensional fractional order hybrid BVPs with integral boundary conditions by an application of n-fixed point theorem, J. Anal., (2021).
  • [43] K. R. Prasad, M. Khuddush, and D. Leela, Existence, uniqueness and Hyers–Ulam stability of a fractional order iterative two-point boundary value Problems, Afr. Mat., (2021).
  • [44] K. R. Prasad, D. Leela, and M. Khuddush, Existence and uniqueness of positive solutions for system of (p, q, r)- Laplacian fractional order boundary value problems, Adv. Theory Nonlinear Anal. Appl., 5(1) (2021), 138-157.
  • [45] A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Differ. Uvavn., 2 (1964), 115-134.
  • [46] A. I. Perov and A. V. Kibenko, On a certain general method for investigation of boundary value problems, Izvestiya Ros-siiskoi Akademii Nauk. Seriya Matematicheskaya, 30 (1996), 249-264.
  • [47] R. Precup and A. Viorel, Existence results for systems of nonlinear evolution equations, International Journal of Pure and Applied Mathematics, 47 (2008), 199-206.
  • [48] T. M. Rus, Ulam stabilities of ordinary differential equations in a Banach space, Carapathian Journal of Mathe- matics, 26 (2010), 103-107.
  • [49] I. Slimane and Z. Dahmani, A continuous and fractional derivative dependance of random differential equations with nonlocal conditions, Journal of Interdisciplinary Mathematics, 24(6) (2021), 1457-1470.
  • [50] R. S. Varga, Matrix Iterative Analysis, Springer Series in Computational Mathematics, Springer: Berlin, Germany, Volume 27, 2000.
  • [51] D. W. J. Victor and M. Khuddush, Existence of solutions for n-dimensional fractional order bvp with -point boundary conditions via the concept of measure of noncompactness, Advanced Studies: Ero-Tbilisi Mathematical Journal 15(1) (2022), 19-37.
  • [52] H. Yfrah, Z. Dahmani, L. Tabharit, and L. Abdelnebi, High order random fractional differential equations: exis- tence, uniqueness and data dependence, J. Interdisciplinary Mathematics, 24(8) (2021), 2121-2138.
آمار
تعداد مشاهده مقاله: 215
تعداد دریافت فایل اصل مقاله: 523


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب