An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

Abstract

In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

Two hybrid and non-hybrid k-dimensional inclusion systems via sequential fractional derivatives

“…with three-point integro-derivative boundary conditions q(0) = 0, q (0) + q (0) = 0, q(1) + R I 0.32 q(0.4) = 0, (24) for all s ∈ [0, 1], where c D j is the Caputo derivative of order j ∈ {2. S s, q(s), q (s), q (s) = 0, 2e s 8 cos q(s), -2e s 8 q (s) sin q(s), -2e s 8 q (s) sin q(s) + -2e s 8 q (s) cos q(s) and ψ(s) < s for all s > 0.…”

“…After that time, some researchers always sought to discover the relationship between sequential derivatives and fractional derivatives [21][22][23]. The efforts of researchers led to the publication of several articles on the issue of boundary value problems of consecutive fractional derivatives (see, for example, [24][25][26][27][28][29][30]).…”

Existence study of semilinear fractional differential equations and inclusions for multi–term problem under Riemann–Liouville operators

“…In previous works, [3][4][5][6] the authors obtained approximate solutions for some multi-order and multi-term fractional boundary value problems by implementing numerical algorithms and some stability results for a system of coupled fractional differential equations have been presented in Etemad et al 7 and Rezapour et al 8 Also, many papers on the positive solution in a cone have been published recently. [9][10][11][12] For more details and to know all about the various definitions of fractional derivatives and integrals as well as its properties, readers are advised to visit the following books. [13][14][15] Fractional differential equations and inclusions generalize ordinary differential equations and inclusions to arbitrary noninteger orders.…”

A discussion concerning the existence results for the Sobolev-type Hilfer fractional delay integro-differential systems

“…In recent years, mathematical modeling has been upheld by fractional calculus, with a few outcomes, and fractional operators were demonstrated to be a fantastic instrument to depict the hereditary characteristics of different patterns. As of late, this blend has acquired a lot of significance, basically because fractional differential equations have become amazing assets for displaying a few complex wonders in various assorted and boundless fields of science and engineering; readers are referred to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and articles [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Hilfer [38] initiated another kind of derivative, along with Riemann-Liouville and Caputo fractional derivative.…”