What is the ruling on saving anime (cartoon) images for enjoyment on a mobile phone, knowing that they are not for necessity, are not published, and are not indecent?

It is impermissible to depict living beings (animate objects), and this includes cartoon images. It is also not allowed to keep them on electronic devices such as mobile phones. Some scholars, like Ibn Uthaymeen, have permitted cartoon images that do not violate creed or morals, but it is more virtuous to avoid them as a matter of piety. The prohibition applies to complete images of living beings. However, drawing only a part of the body (such as the face only, or a body without a head) is permissible, because it is not considered a complete image of an animal. It is advisable to busy oneself with what is more beneficial in this world and the hereafter.