Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

Multi-Term Fractional Differential Equations with Generalized Integral Boundary Conditions

“…given by Equation 24, has at least one solution. Next, we illustrate Theorem 3 by taking f (t, y) and g(t, y) given by Equation (24). Clearly, Conditions (H 4 ) and (H 5 ) hold true with = 1/90 and k = 1/90.…”

“…Fractional-order initial and boundary value problems, involving different kinds of derivatives such as Riemann-Liouville, Caputo, and Hadamard type, have been studied by many authors. The literature on the topic is rapidly augmented with a variety of interesting and useful results during the past few years (see, for instance, [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and references therein).…”

Numerical solution of time‐fractional singularly perturbed convection–diffusion problems with a delay in time

“…They defined the local fractional derivative and extended the matched asymptotic expansion method based on the properties of a local fractional derivative. In Sayevand and Pichaghchi, 31 they introduced a linear B‐spline operational matrix of fractional derivative for singularly perturbed ODEs and PDEs. In this work, we are interested in studying delay parabolic and time‐fractional singularly perturbed PDEs.…”

Existence theory for fractional differential equations with non-separated type nonlocal multi-point and multi-strip boundary conditions

“…The literature on the topic includes the existence and uniqueness results related to classical, periodic/anti-periodic, nonlocal, multi-point, and integral boundary conditions, for instance, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”