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Second-order abstract Cauchy problem of conformable fractional type | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 94، دوره 13، شماره 2، مهر 2022، صفحه 1143-1150 اصل مقاله (378.53 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.20527.2163 | ||
| نویسندگان | ||
| Roshdi Khalil1؛ Sharifa Alsharif* 2؛ Sara Khamis3 | ||
| 1Department of Mathematics, Jordan University, Amman, Jordan | ||
| 2Department of Mathematics, Yarmouk University, Irbid, Jordan | ||
| 3Department of Mathematics, Lusail University, Doha, Qatar | ||
| تاریخ دریافت: 12 خرداد 1399، تاریخ بازنگری: 20 مرداد 1399، تاریخ پذیرش: 07 مهر 1399 | ||
| چکیده | ||
| In this paper, we discuss atomic solutions of the second-order abstract Cauchy problem of conformable fractional type \begin{eqnarray*} u^{(2\alpha )}(t)+Bu^{(\alpha )}(t)+Au(t) &=&f(t) \\ u(0) &=&u_{0}, \\ u^{(\alpha )}(0) &=&u_{0}^{(\alpha )}, \end{eqnarray*}% where $A,B$ are closed linear operators on a Banach space $X,$ $f$ $ :[0,\infty )\rightarrow X$ \ is continuous and $u$ is a continuously differentiable function on $[0,\infty )$. Some new results on atomic solutions using tensor product technique are obtained. | ||
| کلیدواژهها | ||
| Inverse problem؛ fractional derivative؛ tensor product of Banach spaces؛ atomic solution | ||
| مراجع | ||
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[1] M. Abu Hammad and R. Khalil, Systems of linear fractional differential equations, Asian J. Math. Comput. Res. 12 (2016), no. 2, 120–126. [2] T. Abdeljawad, M. Al Horani and R. Khalil, Conformable fractional semigroups of operators, J. Semigroup Theory Appl. 2015 (2015), (1-9) Article ID 7. [3] M. Al Horani, M. Abu Hammad and R. Khalil, Variation of parameters for local nonhomogeneous linear differential equations, J. Math. Comp. Sci. 16 (2016), 147–153. [4] M. Al Horani, An identification problem for some degenerate differential equations, Le Matematiche 57 (2002), 217–227. [5] Sh. Al-Sharif, A. Malkawi, Modification of conformable fractional derivative with classical properties. Ital. J. Pure Appl. Math. 44 ( 2020), 30–39. [6] D. Anderson and D. Ulness, Newly defined conformable derivatives, Adv. Dyn. Syst. Appl. 10(2015), no. 2, 109–137. [7] E. Boyce and C. Di Prima, Elementary differential equations and boundary value problems, 9th ed. John Wiley and Sons, Inc, 2008. [8] R.W. Carroll and R.E. Showalter, Singular and Degenerate Cauchy Problem, Academic Press, New York, San Francisco, London, 1976. [9] W. Deeb and R. Khalil, Best approximation in L(X,Y), Math. Proc. Camb. Phil. Soc. 104 (1988), 527–531. [10] W. Deeb and R. Khalil, Best approximation in Lp (I, X), 0 < p < 1, J. Approx. Theory 58 (1989), no. 1, 68–77. [11] N. Dunford and J. Schwartz, Linear operators, Part I, General theory, Interscience Pub. New York, 1958. [12] A. Favini and A. Yagi, Degenerate differential equations in Banach spaces, Dekker, New York, Basel-Hong Kong, 1999. [13] D. Hussein and R. Khalil, Best approximation in tensor product space, Soochow J. Math. 18 (1982), no. 4, 397–407. [14] R. Khalil and L. Abdullah, Atomic solution of certain inverse problems, Eur. J. Pure Appl. Math. 3 (2010), no. 4, 725–729. [15] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70. [16] S. Khamis, M. Al Horani and R. Khalil, Rank two solutions of the abstract Cauchy problem, J. Semigroup Theory Appl. 2018 (2018), Article ID 3. [17] A. Kilbas, H. Srivastava and J. Trujillo, Theory and applications of fractional differential equations, Math. Studies 204, North-Holland, New York, 2006. [18] W. Light and E. Cheney, Approximation theory in tensor product spaces, Lecture Notes in Mathematics, 1169, Springer Verlag, Berlin, New York, 1985. [19] G. Samko, A. Kilbas and A. Marichev, Fractional integrals and derivatives, theory and applications, Gordon and Breach, Yverdon, 1993. [20] B. Thaller and S. Thaller, Factorization of degenerate Cauchy problem, the linear case, J. Oper. Theory 36 (1996), 121–146. [21] A. Ziqan, M. Al Horani and R. Khalil, Tensor product technique and the degenerate homogeneous abstract Cauchy problem, J. Appl. Funct. Anal. 5 (2010), no. 1, 121–138. [22] A. Ziqan, M. Al Horani and R. Khalil, Tensor product technique and non-homogeneous degenerate abstract Cauchy problem, Int. J. Appl. Math. Res. 23 (2010), no. 1, 137–158. | ||
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