Integral equations and initial value problems for nonlinear differential equations of fractional order

Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

“…Indeed fractional calculus tools have numerous applications in nanotechnology, control theory, viscoplasticity flow, biology, signal and image processing etc, see the latest monographs, [9], [10], [11], [12], [13] articles [14], [15] and reference therein. The mathematical analysis of initial and boundary value problems (linear or nonlinear) of fractional differential equations has been studied extensively by many authors, we refer to [16], [17] , [18], [19], [20] and references therein.…”

On the existence of solutions of fractional integro-differential equations

“…In [11], Clément et al proved the existence of Hölder continuous solutions for a partial fractional differential equation and in [18], Kilbas et al studied the existence of solutions of several classes of ordinary fractional differential equations. Also, Samko et al [35], Anguraj et al [4], Baleanu and Mustafa [9], Diethelm and Ford [15], Kilbas and Marzan [17], Kosmatov [21], Tian and Bai [39], Wei et al [40], Aghajani et al [3], Pilipović and Stojanović [30], Yuste and Acedo [41], Idczak and Kamocki [16], and Kostić [22], between so many more, have investigated the existence of solutions for various types of fractional differential and integral equations. Furthermore, several analytical and numerical methods have been proposed for approximate solutions of fractional differential equations, e.g.…”

Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators

“…There has been a significant development in fractional differential equations (e.g., [1][2][3][4][5][6][7][8][9]). In the previous papers, some authors investigated fractional order partial differential equations [10][11][12][13][14][15].…”