Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel-Reference-Cited by-同舟云学术

Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel

Published:2023 Issue:4 Volume:8 Page:7766-7786
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Kalsoom Amna¹,Afsheen Sehar¹,Azam Akbar²,Ali Faryad³

Affiliation:

1. Department of Mathematics and Statistics, International Islamic University, H-10, 44000, Islamabad, Pakistan

2. Department of Mathematics, Grand Asian University, 7KM Pasrur Road, Sialkot, 51310, Punjab, Pakistan

3. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O.Box 90950, Riyadh, 11623, Saudi Arabian

Abstract

<abstract><p>In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference46 articles.

1. K. S. Miller, B. Ross, An introduction to fractional calculus and fractional diffrential equations, New York: Wiley, 1993.

2. K. B. Oldham, J. Spanier, The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, Elsevier, 1974.

3. D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), 609–625. https://doi.org/10.1006/jmaa.1996.0456

4. S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl., 252 (2000), 804–812. https://doi.org/10.1006/jmaa.2000.7123

5. A. Babakhani, V. Daftardar-Gejji, Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., 278 (2003), 434–442. https://doi.org/10.1016/S0022-247X(02)00716-3