2020
DOI: 10.18576/pfda/060306
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Generalized Fractional Sturm-Liouville and Langevin Equations Involving Caputo Derivative with Nonlocal Conditions

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Cited by 12 publications
(3 citation statements)
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“…In the last three decades, fractional calculus has been attracting the interest of many authors in several fields for the sake of a better description of chaotic complex systems, for example, dynamic systems, rheology, electrical networks, blood-flow phenomena, biophysics, and qualitative theories; see for more details [1,14,19,22,[26][27][28][29]. In order to realize and describe the real phenomena in the fields of science and engineering, some researchers have developed fractional calculus to singular and nonsingular kernels.…”
Section: Introductionmentioning
confidence: 99%
“…In the last three decades, fractional calculus has been attracting the interest of many authors in several fields for the sake of a better description of chaotic complex systems, for example, dynamic systems, rheology, electrical networks, blood-flow phenomena, biophysics, and qualitative theories; see for more details [1,14,19,22,[26][27][28][29]. In order to realize and describe the real phenomena in the fields of science and engineering, some researchers have developed fractional calculus to singular and nonsingular kernels.…”
Section: Introductionmentioning
confidence: 99%
“…Comparing with integer derivatives, the most essential benefit of fractional derivatives is that it describes the quality of a heredity and memory of diverse materials and processes. For more important points about fractional calculus and its applications, we refer to these works [1–10, 49, 50], and the references given therein. Probably, sometimes the nonlocal fractional operators via a singular kernel cannot describe the complicated dynamics systems.…”
Section: Introductionmentioning
confidence: 99%
“…In much of the literature we can see various complicated fractional modelings in which one of the well-known fractional Caputo or the Riemann-Liouville operators has been utilized (see for example, [1][2][3][4][5][6][7][8][9][10][11][12][13]). Also, some generalizations of these operators such as the Hadamard, Caputo-Hadamard and Hilfer fractional operators were utilized by other researchers in the next period and different modelings are investigated using these new operators (see, for instance, [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]).…”
Section: Introductionmentioning
confidence: 99%